CUET Preparation Today
$\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x$ is equal to: |
$\cot \left(e^x\right)+c$, where c is a constant $\tan \left(x e^x\right)+c$, where c is a constant $\cot \left(x e^{x}\right)+c$, where c is a constant $\tan \left\{e^x(1+x)\right\}+c$, where c is a constant |
$\tan \left(x e^x\right)+c$, where c is a constant |
The correct answer is Option (2) → $\tan \left(x e^x\right)+c$, where c is a constant $I=\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx$ let $y=xe^x$ $dy=e^x(1+x)dx$ $⇒I=\int\sec^2ydy=\tan y+c$ $=\tan(xe^x)+c$ |
