Which identity is useful for reducing \(\sin^2 x\) in an even-power integral?

Which identity rewrites \(\tan^2 x\) in terms of \(\sec^2 x\)?

Evaluate \(\int \sin x\,dx\).

Evaluate \(\int \sec^2 x\,dx\).

Evaluate \(\int \cos^2 x\,dx\).

Evaluate \(\int \sin^2 x\,dx\).

Evaluate \(\int \sin^3 x\,dx\).

Evaluate \(\int \cos^3 x\,dx\).

Evaluate \(\int \tan^2 x\,dx\).

Evaluate \(\int \sin^2 x\cos x\,dx\).

Evaluate \(\int \sin^3 x\cos^2 x\,dx\).

Evaluate \(\int \sin^2 x\cos^3 x\,dx\).

Evaluate \(\int \sin^4 x\,dx\).

Evaluate \(\int \cos^4 x\,dx\).

Evaluate \(\int \tan^3 x\,dx\).

Evaluate \(\int \sec^4 x\,dx\).

Evaluate \(\int \sin^5 x\,dx\).

A student says \(\int \sin^2x\,dx=\frac{\sin^3x}{3}+C\). Diagnose the error and give the correct answer.

Derive a reduction formula for \(I_n=\int \sin^n x\,dx\) for \(n>1\).

Evaluate \(\int \sin^2x\cos^2x\,dx\) using a double-angle identity.