eˣ 1-sinx/1-cosx,Integrate the given function w.r.t. x considering them well defined over proper domains.
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HELLO DEAR,
GIVEN:-
∫e^x(1 - sinx)/(1 - cosx).dx
=> I = ∫e^x(1 - sinx)/{2sin²(x/2)}.dx
=> I = ∫e^x{1/2sin²(x/2) - 2sin(x/2)cos(x/2)/2sin²(x/2)}.dx
=> I = ∫e^x{cosec²(x/2)/2 - cot(x/2)}.dx
we know if integral is in the form of e^t{f(t) + f'(t)} then your integral is e^t{f(t)} + C.
therefore, I = -e^x{cot(x/2)} + C.
I HOPE ITS HELP YOU DEAR,
THANKS
GIVEN:-
∫e^x(1 - sinx)/(1 - cosx).dx
=> I = ∫e^x(1 - sinx)/{2sin²(x/2)}.dx
=> I = ∫e^x{1/2sin²(x/2) - 2sin(x/2)cos(x/2)/2sin²(x/2)}.dx
=> I = ∫e^x{cosec²(x/2)/2 - cot(x/2)}.dx
we know if integral is in the form of e^t{f(t) + f'(t)} then your integral is e^t{f(t)} + C.
therefore, I = -e^x{cot(x/2)} + C.
I HOPE ITS HELP YOU DEAR,
THANKS
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