高数题（请把答案用图片的形式上传，过程要详细点，谢谢！）
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∫xe^arctanxdx/(1+x^2)^(3/2)
x=tanu dx=secu^2 cosu=1/√1+x^2) sinu= x/√(1+x^2)
=∫e^u tanusecu^2du/secu^3
=∫e^utanucosudu
=∫e^usinudu=(1/2)e^u(sinu-cosu)+C=(1/2)e^arctanx *(x-1)/√(1+x^2) +C
∫e^usinu
=∫sinude^u
=e^usinu-∫e^ucosudu
=e^usinu-∫cosude^u
=e^usinu-e^ucosu-∫e^usinudu
2∫e^usiudu=e^u(sinu-cosu)
∫e^usinu=(1/2)e^u(sinu-cosu)
x=tanu dx=secu^2 cosu=1/√1+x^2) sinu= x/√(1+x^2)
=∫e^u tanusecu^2du/secu^3
=∫e^utanucosudu
=∫e^usinudu=(1/2)e^u(sinu-cosu)+C=(1/2)e^arctanx *(x-1)/√(1+x^2) +C
∫e^usinu
=∫sinude^u
=e^usinu-∫e^ucosudu
=e^usinu-∫cosude^u
=e^usinu-e^ucosu-∫e^usinudu
2∫e^usiudu=e^u(sinu-cosu)
∫e^usinu=(1/2)e^u(sinu-cosu)
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