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.

IC
Answered by Ionut-Catalin C. Maths tutor

8589 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can you integrate the function (5x - 1)/(x^(3)-x)?


The line L1 has vector equation,  L1 = (  6, 1 ,-1  ) + λ ( 2, 1, 0). The line L2 passes through the points (2, 3, −1) and (4, −1, 1). i) find vector equation of L2 ii)show L2 and L1 are perpendicular.


Maths


If y = (1+3x)^2, what is dy/dx?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences