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Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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