Question

Evaluate the integral using integration by parts: ∫7sin⁻¹(x) dx

Answer 1

To evaluate the integral ∫7sin⁻¹(x) dx using integration by parts, we can use the formula ∫u dv = uv - ∫v du.

Step-by-step explanation:

To evaluate the integral ∫7sin⁻¹(x) dx using integration by parts, we can use the formula ∫u dv = uv - ∫v du. Let's choose u = sin⁻¹(x) and dv = 7 dx. Differentiating u, we get du/dx = 1/√(1-x²), and integrating dv, we get v = 7x. Substituting these values into the integration by parts formula, we have:

∫7sin⁻¹(x) dx = 7x sin⁻¹(x) - ∫7x (1/√(1-x²)) dx

We can now simplify and evaluate the remaining integral.