The value of int sec^3 x , dx is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $I = \int \sec^3 x \, dx = \int \sec x \cdot \sec^2 x \, dx$. Using integration by parts,taking $u = \sec x$ and $dv = \sec^2 x \, dx$,we have

Vedclass · Accepted Answer

$\frac{1}{2} [\sec x 	an x + \log |\sec x + 	an x|] + C$

Vedclass · Answer

(A) Let $I = \int \sec^3 x \, dx = \int \sec x \cdot \sec^2 x \, dx$. Using integration by parts,taking $u = \sec x$ and $dv = \sec^2 x \, dx$,we have $du = \sec x 	an x \, dx$ and $v = 	an x$. $I = \sec x 	an x - \int 	an x (\sec x 	an x) \, dx$ $I = \sec x 	an x - \int \sec x 	an^2 x \, dx$ $I = \sec x 	an x - \int \sec x (\sec^2 x - 1) \, dx$ $I = \sec x 	an x - \int \sec^3 x \, dx + \int \sec x \, dx$ $I = \sec x 	an x - I + \log |\sec x + 	an x|$ $2I = \sec x 	an x + \log |\sec x + 	an x|$ $I = \frac{1}{2} [\sec x 	an x + \log |\sec x + 	an x|] + C$.

The value of $\int \sec^3 x \, dx$ is

Similar Questions

If $I_m = \int x^m \cos n x \, dx = g(x) - \frac{m(m-1)}{n^2} I_{m-2}$, then $g(x) = $

If the primitive of $\cos(\log x)$ is $f(x)\{\cos(g(x)) + \sin(h(x))\}$,then which among the following is true?

$\int x \sec^2 x \, dx = $

$\int \frac{\cot^{-1}(e^x)}{e^x} dx$ is equal to:

$\int \tan^{-1} \left( \frac{2x}{1 - x^2} \right) dx = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module