Practicing Success
$\int \tan ^3 2 x \sec 2 x d x=$ |
$\sec ^3 2 x+3 \sec 2 x$ $\frac{1}{6}\left[\sec ^3 2 x-3 \sec 2 x\right]$ $\left[\sec ^3 2 x-3 \sec 2 x\right]$ none of these |
$\frac{1}{6}\left[\sec ^3 2 x-3 \sec 2 x\right]$ |
$I=\int \tan ^2 2 x \tan 2 x \sec 2 x d x=\int\left(\sec ^2 2 x-1\right) \sec 2 x \tan 2 x d x $ Put $\sec 2 x=t$ ∴ $2 \sec 2 x \tan 2 x dx=dt $ ∴ $I=\frac{1}{2} \int\left(t^2-1\right) d t=\frac{1}{2}\left(\frac{t^3}{3}-t\right)=\frac{1}{6}\left(\sec ^3 2 x-3 \sec 2 x\right)$ Hence (2) is the correct answer. |