Q.10 Evaluate : displaystyle∫e^x(1+x) dx/sin²(xe^x)

Answer: -cot(xe^x)+c Put xe^x=t . Then (xe^x+e^x)dx=dt , i.e. e^x(1+x)dx=dt . I=displaystyle∫dt/sin²t=∫cosec²t dt=-cot t+c=-cot(xe^x)+c .

Evaluate : \(\displaystyle\int\dfrac{e^x(1+x)\,dx}{\sin^2(xe^x)}\)

Q.10 Evaluate : \(\displaystyle\int\dfrac{e^x(1+x)\,dx}{\sin^2(xe^x)}\)

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

Best answer

Answer: \(-\cot(xe^x)+c\)

Put \(xe^x=t\). Then \((xe^x+e^x)dx=dt\), i.e. \(e^x(1+x)dx=dt\).

\(I=\displaystyle\int\dfrac{dt}{\sin^2t}=\int\operatorname{cosec}^2t\,dt=-\cot t+c=-\cot(xe^x)+c\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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