Evaluate the integral I=∫0πθsinθ4+cos2θdθI = \int_{0}^{\pi} \frac{\theta \sin \theta}{4 + \cos^2 \theta} d\thetaI=∫0π4+cos2θθsinθdθ.
π25ln(2+5)\frac{\pi}{2 \sqrt{5}} \ln(2+\sqrt{5})25πln(2+5)
π3arctan(13)\frac{\pi}{\sqrt{3}} \arctan(\frac{1}{\sqrt{3}})3πarctan(31)
π225\frac{\pi^2}{2 \sqrt{5}}25π2
πln(3)\pi \ln(3)πln(3)