Integrate \int \tan^{5x} dx. What is the integral of (e^x)/(e^(2x) + 1) dx? What is the integral of sin^7 x cos^5 x dx? If f(x) = integral e^x dx and f (0) = 2, then what is f(2)? a) e^2. b) e^2 - 1. c) e^2 + 1. d) e + 2. ...
Since secant and tangent both have odd powers, it might be wise to reserve one of each for the derivative of secant and convert everything else to secant. Answer and Explanation:1 Rewrite the integral. {eq}\displaystyle \int \tan^5 x \sec^5 x \, dx \\ = \displaystyle \int \tan^...
Calculate the Integral of … CLR+–×÷^√f(x)π() √3√4√n√ You can also input: •sqrt(…) •root(n, …) lnlog10lognexpexabs|x| sincostancscseccot arcsinsin-1arccoscos-1arctantan-1 arccsccsc-1arcsecsec-1arccotcot-1 ...
5.Evaluate the remaining integral: The integral∫ln|cos(x)|dxdoes not have a simple closed form, but it can be expressed in terms of known functions or evaluated numerically if needed. 6.Final result: The integral can be expressed as: ...
Integral of sec(x)*tan(x) by x: 1/cos(x)+C To compute the integral of sec(x) * tan(x) with respect to x, follow these steps: 1.Identify the integral: We want to compute the integral 2.Recall the derivative: Recognize that the derivative of sec(x) is sec(x) * tan(x). Th...
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arctan(3x)x−16∫1uduarctan(3x)x-16∫1uduThe integral of 1u1u with respect to uu is ln(|u|)ln(|u|). arctan(3x)x−16(ln(|u|)+C)arctan(3x)x-16(ln(|u|)+C)Simplify. arctan(3x)x−16ln(|u|)+Carctan(3x)x-16ln(|u|)+CReplace...
Answer to: Evaluate the integral. (Use C for the constant of integration.) Integral of tan^5(4x) sec^4(4x) dx. By signing up, you'll get thousands...
Find the Derivative y = integral from 0 to tan(x) of 1/(1+t^2) with respect to t( y=(
Ahmed's Integral∫01tan−1(x2+2)(x2+2)(x2+1)dx 方法一: 令I=∫01tan−1(2+x2)(1+x2)2+x2dx 及 f(t)=∫01tan−1(t2+x2)(1+x2)2+x2dx 其中f(1)=I. ⇒f′(t)=∫01dx(1+x2)2+x2ddttan−1(t2+x2)=∫01dx(1+x2)2+x22+x21+(t2+x2)2=...