Q.14 Evaluate: ∫e^x(1 + x)/cos²(xe^x) dx

Answer: tan(xe^x) + c Put xe^x = t . Then (xe^x + e^x) dx = dt , i.e. e^x(1 + x) dx = dt . ∫dt/cos² t = ∫sec² t dt = tan t + c = tan(xe^x) + c .

Evaluate: \(\int\frac{e^x(1 + x)}{\cos^2(xe^x)}\,dx\)

Q.14 Evaluate: \(\int\frac{e^x(1 + x)}{\cos^2(xe^x)}\,dx\)

Doubtly Asked 28 Oct 2026 Board exam · June 2026 hsc 12th Save WhatsApp Report

Best answer

Answer: \(\tan(xe^x) + c\)

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

\(\int\frac{dt}{\cos^2 t} = \int\sec^2 t\,dt = \tan t + c = \tan(xe^x) + c\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?