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evaluate the following integral ∫ 1 / (sqrt(1 – x^2) ( 2 + 3 sin^-1 (x)) dx

evaluate the following integral
∫ 1 / (sqrt(1 – x^2) ( 2 + 3 sin^-1 (x)) dx

Grade:12

1 Answers

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

I = \int \frac{1}{\sqrt{1-x^{2}}(2+3sin^{-1}x)}dx
2+3sin^{-1}x = t
\frac{3}{\sqrt{1-x^2}}dx = dt
I = \frac{1}{3}\int \frac{dt}{t}
I = \frac{logt}{3} + c
I = \frac{log(2+3sin^{-1}x)}{3} + c

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