What is #int x^3 * sqrt(x^2 + 4)dx#?
2 Answers
Use the substitution
Explanation:
For this problem we will use:
-
#intx^ndx = x^(n+1)/(n+1) + C# -
#int(f(x) + g(x))dx = intf(x)dx + intg(x)dx#
We will proceed using the substitution
Then
Use
Explanation:
Let
Differentiate with respect to
Also we have
Rewriting our integral as
Substituting for
We apply power rule
It can be further simplified if needed.