1 / | | x*asin(x) dx | / 0
Integral(x*asin(x), (x, 0, 1))
Use integration by parts:
Let and let .
Then .
To find :
The integral of is when :
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
SqrtQuadraticDenomRule(a=1, b=0, c=-1, coeffs=[1, 0, 0], context=x**2/sqrt(1 - x**2), symbol=x)
So, the result is:
Add the constant of integration:
The answer is:
________ / 2 / 2 | asin(x) x *asin(x) x*\/ 1 - x | x*asin(x) dx = C - ------- + ---------- + ------------- | 4 2 4 /
Use the examples entering the upper and lower limits of integration.