int frac{(1+x) e^x}{cot left(x e^xright)} d x | vedclass

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

Question

(C) Let $I = \int \frac{(1+x) e^x}{\cot \left(x e^x\right)} d x$. Substitute $t = x e^x$. Differentiating with respect to $x$,we get $dt = (e^x + x e^

Vedclass · Accepted Answer

$\log \left(\sec \left(x e^x\right)\right)+c$

Vedclass · Answer

(C) Let $I = \int \frac{(1+x) e^x}{\cot \left(x e^xight)} d x$. Substitute $t = x e^x$. Differentiating with respect to $x$,we get $dt = (e^x + x e^x) dx = e^x(1+x) dx$. Substituting these into the integral,we get $I = \int \frac{dt}{\cot t} = \int 	an t dt$. The integral of $	an t$ is $\log |\sec t| + c$. Thus,$I = \log |\sec(x e^x)| + c$. Therefore,the correct option is $C$.

$\int \frac{(1+x) e^x}{\cot \left(x e^x\right)} d x=$

Similar Questions

$\int {\frac{{\sqrt {{x^2} + 1} [\log ({x^2} + 1) - 2\log x]}}{{{x^4}}}} dx$ is equal to

$\int 3^{3^x} \cdot 3^x \, dx =$

$\int \sin^3 x \cos^2 x \, dx = $

Evaluate the integral: $\int \frac{\cos ^4 x}{\left(\sin ^2 x+\sin ^{-3} x \cos ^5 x\right)^3} d x$

$\int \sqrt{\sin x} \cos x \, dx = \frac{2}{3}(\sin x)^{3/2} + C$ is valid when $x$ lies in the interval

Vedclass Test Series

Exam Paper Generator

Online Exam Module