The value of int frac{(x-1) e^x}{(x+1)^3} ,d | vedclass

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

Question

(B) Let $I = \int \frac{(x-1) e^x}{(x+1)^3} \,d x$ We can rewrite the numerator as $(x+1-2)$: $I = \int \frac{(x+1-2) e^x}{(x+1)^3} \,d x$ $I = \int e

Vedclass · Accepted Answer

$\frac{e^x}{(x+1)^2}+c$,(where $c$ is constant of integration)

Vedclass · Answer

(B) Let $I = \int \frac{(x-1) e^x}{(x+1)^3} \,d x$ We can rewrite the numerator as $(x+1-2)$: $I = \int \frac{(x+1-2) e^x}{(x+1)^3} \,d x$ $I = \int e^x \left[ \frac{x+1}{(x+1)^3} - \frac{2}{(x+1)^3} \right] d x$ $I = \int e^x \left[ \frac{1}{(x+1)^2} - \frac{2}{(x+1)^3} \right] d x$ Let $f(x) = \frac{1}{(x+1)^2} = (x+1)^{-2}$. Then $f'(x) = -2(x+1)^{-3} = -\frac{2}{(x+1)^3}$. Using the standard integral formula $\int e^x [f(x) + f'(x)] \,d x = e^x f(x) + c$: $I = e^x \left( \frac{1}{(x+1)^2} \right) + c = \frac{e^x}{(x+1)^2} + c$.

The value of $\int \frac{(x-1) e^x}{(x+1)^3} \,d x$ is equal to

Similar Questions

$\int e^x \left( \frac{1 + \sin x}{1 + \cos x} \right) dx = $ . . . . . . $+ c$.

If $\int e^x \left( \frac{x^2-8x+19}{(x-1)^5} \right) dx = \frac{e^x(lx+m)}{(x-1)^4} + C$, then $4l+m=$

$\int [\sin(\log x) + \cos(\log x)] dx = $

$\int_{\pi/4}^{\pi/2} e^x (\log \sin x + \cot x) \, dx = $

$\int {{e^x}(1 - \cot x + {{\cot }^2}x)\,dx} $ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module