Evaluate the following integrals: ∫ (sin^-1 x)/x^2 dx

Question

Evaluate the following integrals:

\(\int \frac{sin^{-1}x}{x^2}dx\)

∫ (sin^-1x)/x² dx

Answer 1

Tip – If f₁(x) and f₂(x) are two functions , then an integral of the form ∫ f₁(x)f₂(x)dx can be INTEGRATED BY PARTS as

where f₁(x) and f₂(x) are the first and second functions respectively.

Taking f₁(x) = sin^-1x and f₂(x) = 1/x²,

where c is the integrating constant.