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if integration of (a/(b+ce^x)) is = -k(ln(mod(b+ce^x)-x)+d then what is the k value?

if integration of (a/(b+ce^x)) is = -k(ln(mod(b+ce^x)-x)+d then what is the k value?

Grade:12th pass

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
integral a/(b+ce^x) dx
put b+ce^x=t
on diff.w.r.t. x, we get
ce^x dx=dt
integral adt/ce^x.t
=integral a dt/t(t-b)
=a/bintegral[1/(t-b)-1/t]dt
=a/b[log(mod(t-b))-log(mod(t))]+d
=a/b[log(mod(ce^x))-log(mod(b+ce^x))]+d
=a/b[cx-log(mod(b+ce^x))]+d
=-a/b[log(mod(b+ce^x))-cx]+d
comparing the result to the right hand side of the question , it is clear that K=a/b Ans.

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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