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Integrate ∫sin(lnx)dx Please reply soon.

Integrate
∫sin(lnx)dx
Please reply soon.

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int sin(lnx)dx
lnx = t
\frac{1}{x}.dx = dt
I = \int e^{t}.sin(t)dt
Use ILATE rule, we have
I = e^{t}(sint - cost) + c
I = x(sin(lnx) - cos(lnx)) + c
Lovey
10 Points
7 years ago
Thank u very much.

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