If int e^x(1+x) cdot sec ^2(x e^x) , dx = f(x | vedclass

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

Question

(D) Given the integral: $\int e^x(1+x) \cdot \sec^2(x e^x) \, dx = f(x) + C$. Let $t = x e^x$. Differentiating both sides with respect to $x$,we get:

Vedclass · Accepted Answer

$	an(x e^x)$

Vedclass · Answer

(D) Given the integral: $\int e^x(1+x) \cdot \sec^2(x e^x) \, dx = f(x) + C$. Let $t = x e^x$. Differentiating both sides with respect to $x$,we get: $\frac{dt}{dx} = e^x + x e^x = e^x(1+x)$. Thus,$dt = e^x(1+x) \, dx$. Substituting these into the integral,we get: $\int \sec^2(t) \, dt$. The integral of $\sec^2(t)$ is $	an(t) + C$. Replacing $t$ with $x e^x$,we get: $	an(x e^x) + C$. Comparing this with $f(x) + C$,we find $f(x) = 	an(x e^x)$.

If $\int e^x(1+x) \cdot \sec ^2(x e^x) \, dx = f(x) + \text{constant}$,then $f(x)$ is equal to

Similar Questions

$\int \frac{\sec x}{\sqrt{\sin (2 x + \theta) + \sin \theta}} d x =$

$\int \frac{x^4+5^{x-1} \cdot \log _e 5}{x^5+5^x} \cdot d x=$ . . . . . . $+C$.

$\int (x + 3)({x^2} + 6x + 10)^9 \, dx$ equals

$\int \frac{dx}{x^2 \sqrt{4+x^2}}$ is equal to

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module