How do you integrate int 1/sqrt(4x+8sqrtx-15) using trigonometric substitution?
1 Answer
May 17, 2018
Use the substitution
Explanation:
Let
I=int1/sqrt(4x+8sqrtx-15)dx
Complete the square in the denominator:
I=int1/sqrt(4(sqrtx+1)^2-19)dx
Apply the substitution
I=1/2int(sqrt19sec^2theta-2sectheta)d theta
Integrate directly:
I=1/2(sqrt19tantheta-2ln|sectheta+tantheta|)+C
Reverse the substitution:
I=1/2sqrt(4x+8sqrtx-15)-ln|2(sqrtx+1)+sqrt(4x+8sqrtx-15)|+C