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

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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 $C$.

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

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