Solve the following integral: ∫ arcsin(x)/sqrt(1-x^2) dx

We will solve the integral by part. We know the formula for integration by parts: ∫ f(x)'g(x)dx=f(x)g(x)-∫f(x)g(x)'dx (1). We know that: (arcsin (x))'=1/sqrt(1-x^2). So we can write arcsin(x)/sqrt(1-x^2) dx =arcsin(x)*(arcsin(x))'. So, in formula (1) f(x)=arcsin(x), g(x) =arcsin(x) and f(x)'g(x)=arcsin(x)/sqrt(1-x^2) dx. So, using (1) we obtain: ∫ arcsin(x)/sqrt(1-x^2) dx=∫ (arcsin(x))'*arcsin(x)dx=(arcsin(x))2-∫ arcsin(x)arcsin(x)'dx=(arcsin(x))2- ∫ arcsin(x)/sqrt(1-x^2) dx. We obtained: ∫ arcsin(x)/sqrt(1-x^2) dx=(arcsin(x))2- ∫ arcsin(x)/sqrt(1-x^2) dx =>2 ∫ arcsin(x)/sqrt(1-x^2) dx=(arcsin(x))2=>∫ arcsin(x)/sqrt(1-x^2) dx=(arcsin(x))2/2.

Answered by Ionut-Catalin C. Maths tutor

8122 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C has equation: 2(x^2)y + 2x + 4y – cos(pi*y) = 17. Use implicit differentiation to find dy/dx in terms of x and y.


integrate e^x sin x dx


Let f(x)= x^3 -9x^2 -81x + 12. Calculate f'(x) and f''(x). Use f'(x) to calculate the x-values of the stationary points of this function.


Line AB, with equation: 3x + 2y - 1 = 0, intersects line CD, with equation 4x - 6y -10 = 0. Find the point, P, where the two lines intersect.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences