Indefinte integration reloaded

akki ~~ unlucky forever ~~

$put\ x=acos\theta\\ \\ I=a^2\ \int_{0}^{\frac{\pi}{2}}\theta^2sin^2\theta\ d\theta\\ \\ or\ I = a^2\ \int_{0}^{\frac{\pi}{2}}cos^2\theta\ (\theta^2+\frac{\pi^2}{4}-\theta\pi)d\theta\\ \\adding\ both\\ \\ I=\frac{a^2}{2}\int_{0}^{\frac{\pi}{2}}(\theta^2+\frac{\pi^2}{4}cos^2\theta-\pi\theta\ cos^2\theta)d\theta$

now,all 3 integrals are easily seperately integrable . . .