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∫xarctanxdx
=∫arctanxdx²/2
=x²/2arctanx-∫x²/2darctanx
=x²/2arctanx-1/2∫x²/(1+x²)dx
=x²/2arctanx-1/2∫(x²+1-1)/(1+x²)dx
==x²/2arctanx-1/2∫1-1/(1+x²)dx
==x²/2arctanx-1/2x+1/2arctanx+c
=∫arctanxdx²/2
=x²/2arctanx-∫x²/2darctanx
=x²/2arctanx-1/2∫x²/(1+x²)dx
=x²/2arctanx-1/2∫(x²+1-1)/(1+x²)dx
==x²/2arctanx-1/2∫1-1/(1+x²)dx
==x²/2arctanx-1/2x+1/2arctanx+c
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