Grade 12th passIntegral Calculus
integratesinx.cosx/(sinx+cosx)^2 with respect to dx
integrate
sinx.cosx/(sinx+cosx)^2 with respect to dx
1 Answer
Anurag Singh
int/sinxcosxdx/(sinx+cosx)(square).
=int/1/2(sin2x/(sinx+cosx)(square))dx.
=int/1/2(sin2x+1-1/1+2sinxcosx)dx.
=int/1/2(dx-1/1+sin2xdx).
=int/x/2dx-1/2int/1/1+sin2xdx.
=x/2-1/2int/(1/1+sin2x))dx.
=x/2-1/2int/{(1/1+sin2x)into( 1-sin2x/1-sin2x) }. (rationalising).
=x/2-1/2(1/cos(square)2x-sin2x/cos(square)2x)dx.
=x/2-1/4tan2x+1/4sec2x+c
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