∫ (x+arctanx)/x^2 dx

∫ (x+arctanx)/x^2 dx
∫ (x+arctanx)/x^2 dx

∫ (x+arctanx)/x^2 dx
∫ (x+arctanx)/x²dx
=-∫ (x+arctanx)d(1/x)
=-(x+arctanx)/x+∫(1/x)d(x+arctanx)
=-(x+arctanx)/x+∫(1/x)[1+1/(1+x²)]dx
=-(x+arctanx)/x+∫1/xdx+∫1/x(1+x²)dx
=-(x+arctanx)/x+ln|x|+∫(1+x²-x²)/x(1+x²)dx
=-(x+arctanx)/x+ln|x|+∫1/xdx-∫x/(1+x²)dx
=-(x+arctanx)/x+2ln|x|-(1/2)∫1/(1+x²)dx²
=-(x+arctanx)/x+2ln|x|-(1/2)ln(1+x²)+C
=-arctanx/x+2ln|x|-(1/2)ln(1+x²)+C

∫ (x+arctanx)/x^2 dx=∫ (1/x）dx+∫ （arctanx)/x^2 dx=lnx+∫ arctanx d(-1/x)=lnx+(-arctanx )/x+∫ {(1/x)-[x/(1+x^2)]}dx=2lnx+(-arctanx )/x-[(1/2)*ln(1+x^2)]+c由∫ arctanx d(-1/x) 到(-arctanx )/x+∫ {(1/x)-[x/(1...

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∫ (x+arctanx)/x^2 dx=∫ (1/x）dx+∫ （arctanx)/x^2 dx=lnx+∫ arctanx d(-1/x)=lnx+(-arctanx )/x+∫ {(1/x)-[x/(1+x^2)]}dx=2lnx+(-arctanx )/x-[(1/2)*ln(1+x^2)]+c

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