Integral (x.sin x) / (1+cos^2 x)

Nur Kholis
help me please!
\displaystyle \int_{0}^{\pi}{\frac{x\sin{x}}{1+\cos^2{x}}{dx}}= ....

 

Faiqa Adzkiya
gini mungkin kak..
misal
\displaystyle \int_{0}^{\pi}{\frac{x\sin{x}}{1+\cos^2{x}}{dx}}= A
maka:
\displaystyle \int_{0}^{\pi}{\frac{x\sin{x}}{1+\cos^2{x}}{dx}}= \int_{0}^{\pi}{\frac{(\pi-x)\sin{x}}{1+\cos^2{x}}{dx}}=A
\displaystyle 2A=\int_{0}^{\pi}{\frac{x\sin{x}}{1+\cos^2{x}}{dx}}
\displaystyle 2A={-\pi}\int_{1}^{-1}{\frac{du}{1+u^2}}
\displaystyle 2A={-\pi}[\arctan{-1}-\arctan{1}]
\displaystyle 2A={-\pi}[-\frac{\pi}{4}-\frac{\pi}{4}]
\displaystyle 2A={-\pi}[-\frac{\pi}{2}]
\displaystyle 2A=\frac{\pi^2}{2}
\displaystyle A=\frac{\pi^2}{4}
soktau.com
hihihi.. ^_^

 

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