This is a question which tests your knowledge of how to use trigonometric identities as well as integration As there is no way to immediately integrate tan^2(x) using well known trigonometric integrals and derivatives, it seems like a good idea would be writing tan^2(x) as sec^2(x) 1Solve 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 CTo integrate tan2x, also written as ∫tan2x dx, and tan 2x, we use the u substitution because the integral of tanu is a standard solution in formula books Let u=2x Then, du/dx=2 We transpose for dx to get the above expression Hence, our new integration can be writtin in terms of u and is simpler to solve
Q45 Integral Of 1 Tan 2x Sec 2x Youtube
Tan^2x antiderivative
Tan^2x antiderivative-Calculate the indefinite integral of the function y = tan^4x tan^2x 2 Educator answers Math Latest answer posted November 23, 10 at AMSee the answer How do you solve this integral of 3 sec(2x1)tan(2x1)?
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Nov 02, · The Second Derivative Of tan(2x) To calculate the second derivative of a function, you just differentiate the first derivative From above, we found that the first derivative of tan(2x) = 2sec 2 (2x) So to find the second derivative of tan(2x), we just need to differentiate 2sec 2 (2x) We can use the chain rule to find the derivative of 2sec 2 (2x) (bearing in mind that the derivativeThe following is a list of integrals (antiderivative functions) of trigonometric functionsFor antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functionsFor a complete list of antiderivative functions, see Lists of integralsFor the special antiderivatives involving trigonometric functions, see Trigonometric integralQuestion How Do You Solve This Integral Of 3 Sec(2x1)tan(2x1)?
This integral is discussed in most calculus books I will write a detailed solution, because thinking about this integral gives a good workout in techniques of integration You have already been told about the useful identity $$1\tan^2 x=\frac{1}{\cos^2 x}$$ You may have seen this identity as $$1\tan^2x =\sec^2 x$$Feb 11, 16 · Rather than saying u = sin x, use u = 2x instead Just expand tan u into ##\frac{sin\, u}{cos\, u}## This integral is much easier to solve Expanding sin 2x and cos 2x in terms of sin x and cos x just makes things more complicatedThe need for antiderivatives arises in many situations, and we look at various examples throughout the remainder of the text Here we examine one specific example that involves rectilinear motion
Nov 10, · The antiderivative of a function \(f\) is a function with a derivative \(f\) Why are we interested in antiderivatives?Dec 08, 16 · Ex 72, 21 tan2 (2𝑥 – 3) Let I = tan2 (2𝑥 – 3) 𝑑𝑥 = sec2 2𝑥 – 3−1 𝑑𝑥 = sec2 2𝑥 – 3 𝑑𝑥− 1𝑑𝑥 = Free integral calculator solve indefinite, definite and multiple integrals with all the steps Type in any integral to get the solution, steps and graph This website uses cookies to ensure you get the best experience
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Interactive 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\\int \tan^{2}x\sec{x} \, dx\ >
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreAug 03, 13 · The chain rule says that after you have differentiated tan(2x) into sec^2(2x), you need to multiply the result by the argument (argument means whatever is inside the bracket In this case, d/dx (2x) =2, so this is the 2 Similarly, the derivative of (2x)^2 is 4x times the derivative of 2x, which is 4x*2, which is 8x1 Proof Strategy The strategy is not obviousMultiply and divide by (sec x tan x);
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Q45 Integral Of 1 Tan 2x Sec 2x Youtube
This problem has been solved!Mar 27, 16 · 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!!!!!=2tanx/1tan^2x as this equation formula 11K views Naveen, Any questions related math, sci, gk, psycho Updated May 4, 21 · Author has 76 answers and 341K answer views t a n 2 x httpsstudyandtrickblogspotcom 19K views · View upvotes 1 Ankit Kumar Mishra
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Jan 02, 21 · In this section we look at how to integrate a variety of products of trigonometric functions These integrals are called trigonometric integralsThey are an important part of the integration technique called trigonometric substitution, which is featured in Trigonometric SubstitutionThis technique allows us to convert algebraic expressions that we may not be ableFind 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 integralCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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