int frac{e^{x}(1+x)}{cos ^{2}(x e^{x})} d x e | vedclass

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

Question

(D) Let $I = \int \frac{e^{x}(1+x)}{\cos ^{2}(x e^{x})} d x$. Substitute $t = x e^{x}$. Differentiating both sides with respect to $x$,we get: $dt = (

Vedclass · Accepted Answer

$	an (x e^{x})+C$

Vedclass · Answer

(D) Let $I = \int \frac{e^{x}(1+x)}{\cos ^{2}(x e^{x})} d x$. Substitute $t = x e^{x}$. Differentiating both sides with respect to $x$,we get: $dt = (e^{x} + x e^{x}) dx = e^{x}(1+x) dx$. Substituting these into the integral: $I = \int \frac{dt}{\cos ^{2} t} = \int \sec ^{2} t dt$. Integrating $\sec ^{2} t$,we get: $I = 	an t + C$. Substituting back $t = x e^{x}$: $I = 	an (x e^{x}) + C$. Thus,the correct option is $D$.

$\int \frac{e^{x}(1+x)}{\cos ^{2}(x e^{x})} d x$ equals

Similar Questions

$\int \frac{d x}{\sqrt{2 e^x-1}}=$

$\int \frac{1}{x^2(x^4 + 1)^{3/4}} dx = $

$\int \frac{\sin x \, dx}{a^2 + b^2 \cos^2 x} = $

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

Integrate the function: $\frac{3x^{2}}{x^{6}+1}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module