How do you find the indefinite integral of ∫ dx / √(x+1) + √(x+1)^3 ?
1 Answer
Apr 16, 2018
Explanation:
We want to solve
I=int1/(sqrt(x)+sqrt((x+1)^3))dx
Rewrite the integrand as
I=int1/((x+1)^(1/2)+(x+1)^(3/2))dx
Make a substitution
I=int1/(u^(1/2)+u^(3/2))du
Make a substitution
I=int(2s)/(s+s^3)ds
color(white)(I)=2int1/(1+s^2)ds
color(white)(I)=2arctan(s)+C
Substitute back
I=2arctan(sqrt(x+1))+C