求不定积分arc乘以tanxdx

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求不定积分arc乘以tanxdx求不定积分arc乘以tanxdx求不定积分arc乘以tanxdx原式=xarctanx-∫xdarctanx=xarctanx-∫xdx/(1+x²)=xar

求不定积分arc乘以tanxdx
求不定积分arc乘以tanxdx

求不定积分arc乘以tanxdx
原式=xarctanx-∫xdarctanx
=xarctanx-∫xdx/(1+x²)
=xarctanx-1/2∫dx²/(1+x²)
=xarctanx-1/2∫d(1+x²)/(1+x²)
=xarctanx-ln(1+x²)/2+C


∫arctanxdx
=xarctanx-∫(x/(x²+1))dx(分部积分法)
=xarctanx-[∫(1/(x²+1))dx²]/2
=xarctanx-1/2∫[1/(1+x²)]d(1+x²)
=xarctanx-ln(1+x²)/2+C(c为常数)