SOLUTION Here only tan x occurs, so we use tan 2x sec 2x 1 to rewrite a tan 2x factor in terms of sec 2x y tan x dx y tan x tan x dx 3 2 y tan x sec 2x 1 dx y tan x sec 2x dx y tan x dx tan 2x 2 ln sec x C In the first integral we mentally substituted u tan x so that du sec 2x dx2 The answer is this but the coefficient is 1 4 Why? · If \(k\) is even and \(j\) is odd, then use \(\tan^2x=\sec^2x−1\) to express \(\tan^kx\) in terms of \(\sec x\) Use integration by parts to integrate odd powers of \(\sec x\) Example \(\PageIndex{8}\) Integrating \(∫\tan^kx\sec^jx\,dx\) when \(j\) is Even
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Tan^2x secx integral-Evaluate integral of 1/(sec(x)^2) with respect to x Simplify Tap for more steps Rewrite as Rewrite as Rewrite in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by Multiply by Use the halfangle formula to rewrite asSubsection 1 Integrating \(\int \tan^m x\sec^n x\dee{x}\) The strategy for dealing with these integrals is similar to the strategy that we used to evaluate integrals of the form \(\int \sin^m x\cos^n x\dee{x}\) and again depends on the parity of the exponents \(n\) and \(m\text{}\)
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The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables You can also check your answers! · Using properties of definite integrals, evaluate the following∫(0>π) (x tanx)/(secxtanx) dx · Integral of u^2 is NOT (u^3)/3 c Rather, integral of (u^2)du = (u^3)/3 c In (tan^2)x your 1st mistake is not writing dx Note that dx is NOT always du!!!!!
Question Find the indefinite integral (Use C for the constant of integration) I see sec 2x tan 2x dx This problem has been solved!Integrate sec^22x To integrate sec^22x, also written as ∫sec 2 2x dx, sec squared 2x, (sec2x)^2, and sec^2 (2x), we start with a u substitution Let u = 2x This is a simple u substitution Therefore du/dx = 2 This is a simple differentiation step We rearrange the previous expression for dxWe can simplify the implementation of the integral with the help of substitution, wherein we allow u= sec2x u = sec 2 x This substitution entails the change in the differential variable and the
The definite integral of from to , denoted , is defined to be the signed area between and the axis, from to Both types of integrals are tied together by the fundamental theorem of calculus This states that if is continuous on and is its continuous indefinite integral, then This means Sometimes an approximation to a definite integral is(Use C for the constant of integration) I see sec 2x tan 2x dx ;\\int \tan^{2}x\sec{x} \, dx\ > <
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Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Functions Line Equations Functions Arithmetic & Comp Conic Sections TransformationSolution for Evaluate the integral S tan (2x) sec°(2x) dx Social Science AnthropologySolution for 11 Evaluate the integral tan 2x dx A In sec 21 C sec² 2x C С In cos 24 C D 2 sec 2x C В
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· Write tan 3 (2x) as tan 2 (2x)tan(2x) = sec 2 (2x)1tan(2x) Now the function is Integral sec 2 (2x)1 tan(2x) sec(2x)dx Put sec(2x) = u sec(2x)tan(2x)dxUse \(\tan^2x=\sec^2x1~(=u^21)\) to replace the leftover tangents \(m\) is even or \(n\) is odd Use either \(1\) or \(2\) (both will work) The power of secant is odd and the power of tangent is even No guideline The integrals \(\ds\int\sec x\,dx\) and \(\ds\int\sec^3 x\,dx\) can usually be looked up, or recalled from memory Example 223Expert Answer Previous question Next question
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See the answer How do you solve this integral of 3 sec(2x1)tan(2x1)?Question How Do You Solve This Integral Of 3 Sec(2x1)tan(2x1)?I = sec 2xdx Multiplying in Nr and Dr by (sec 2xtan 2x ) I = {sec 2x(sec 2x tan 2x)/(sec 2x tan 2x)}dx Let (sec 2x tan 2x) = p then2(sec 2xtan 2x sec^2 2x)dx = dp or, sec 2x(tan 2x sec 2x)dx = 1/2dp I = (1/2)(1/p)dp I = 1/2 log p C I = (1/2) log sec 2x tan 2
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Integrate 2sec^2x tanx To integrate 2sec^2x tanx, also written as ∫2sec 2 x tanx dx, 2 sec squared x tan x, and 2 (sec x)^2 tanx, we start by recognising that the differential of one half is within the other half of the same expressionDifferentiate c and d, use the product rule to find v Then just use the product rule on u and v 0 · Here, notice that sec^2x is already in the integral, and all that remains is tan^2x That is, we have tanx in squared form accompanied by its derivative, sec^2x This integral is ripe for substitution!
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· In general if you vave a power of sec or tan youre gonna have to use tan^2x 1 = sec^2x and d/dx(tanx) = sec^2x and d/dx(secx) = secxtanx Yeah, that's good advice Sec/tan and cosec/cot are almost always related in the questions they give youThey use the key relations sin 2 x cos 2 x = 1 \sin^2x \cos^2x = 1 sin 2 x cos 2 x = 1, tan 2 x 1 = sec 2 x \tan^2x 1 = \sec^2x tan 2 x 1 = sec 2 x, and cot 2 x 1 = csc 2 x \cot^2x 1 = \csc^2x cot 2 x 1 = csc 2 x to manipulate an integral into a simpler formIntegration of tan^2x sec^2x/ 1tan^6x dx Ask questions, doubts, problems and we will help you Integration of tan^2x sec^2x/ 1tan^6x dx Homework Help myCBSEguide
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In the integral inttan^2xsec^2xdx, let u=tanx and du=sec^2xdx This gives us inttan^2xsec^2xdx=intu^2du · Ex 71, 19 sec 2 2 dx sec 2 2 = 1 cos 2 1 sin 2 = 1 cos 2 sin 2 1 = sin 2 cos 2 = tan 2 = sec 2 1 = sec 2Get an answer for '`int (sec^2x)/(tan^2x5tanx6) dx` Use substitution and partial fractions to find the indefinite integral' and find homework help for other Math questions at eNotes
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Solve the integral = ln u C substitute back u=cos x = ln cos x C QED 2 Alternate Form of Result tan x dx = ln cos x C = ln (cos x)1 C = ln sec x CIf you let u=tanx in integral (tan^2)x you get integral u^2 dx which is not (u^3)/3 c since du= sec^2x dxInteractive graphs/plots help visualize and better understand the functions For more about how to use the Integral Calculator, go to "Help" or take a look at the examples
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· Transcript Ex 73, 15 tan3 2 sec 2 Let I= 3 2 sec 2 = tan 2 2 tan 2 sec 2 = sec 2 2 1 2 sec 2 Putting sec 2 = Differentiating wrtx sec 2 = 2 sec 2 tan 2 = = 2 sec 2 tan 2 Putting values of sec 2x and dx in equation I = sec 2 2 1 2 sec 2 = 2 1 2 sec 2 2 sec 2 tan 2 = 2 1 2 = 1 2 2 1 = 1 2 2 1 = 1 2 2 1 2 1 = 1 2 3 3 PuttingKeep breaking it down until you find something you can work with Let u=sec^2 and v=tan^2 and if that's still too much at this stage Let a=sec b=sec c=tan d=tan Differentiate a and b, use the product rule to find u;$$\int \sec^2x \tan^2x dx 2\int \sec^2x \tan^2x dx= tan^2x c, c\in\mathbb{R}$$ Note that once we have a side without an integral on it you need to include a constant of integration I have used $c$ The two expressions on the left hand side are the same so you can add them giving $$3\int \sec^2x \tan^2x dx= tan^2x c$$ So simply divide by 3 to get your answer
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Free integral calculator solve indefinite, definite and multiple integrals with all the steps Type in any integral to get the solution, steps and graphIntegral of tan^2 (x)*sec (x) · 10) \(\displaystyle ∫\tan^2x\sec^2x\,dx\) Compute the following integrals using the guidelines for integrating powers of trigonometric functions Use a CAS to check the solutions (Note Some of the problems may be done using techniques of integration learned previously) 11) \(\displaystyle ∫\sin^3x\,dx\) Answer
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Find the Integral sec(2x)tan(2x) Let Then , so Rewrite using and Tap for more steps Let Find Tap for more steps Differentiate Differentiate using the chain rule, which states that is where and Since is constant with respect to , move out of the integralSee the answer See the answer See the answer done loading Show transcribed image textMy steps ∫ sec 3 ( 2 x) d x Let u = 2 x, then 1 2 d u = d x 1 2 ∫ sec 3
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This problem has been solved!{eq}\int \tan x \sec^2x dx {/eq} Integration by u Substitution We can find the indefinite integrals of some functions by applying the method of usubstitutionIntegral of sec^2x/(secx tanx)^n Functions involving trigonometric functions are useful as they are good at describing periodic behavior This section describes several techniques for finding antiderivatives of certain combinations of trigonometric functions
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· So students this is final answer of integration of sec^x tan^x and as you can see in both of the method answer will be same is secx c Integration of sec^2x integration of secant squared x Let try to solving, in this case we solve the \( \int(sec^2x) dx \) Once again, I = \( \int(sec^2x) dx \) Now multiply tanx/tanx with the sec^2x And we get,
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