How do you integrate by substitution int (x^2+3x+7)/sqrtxdx?

1 Answer
Mar 19, 2017

(2/5)x^(5/2) +2x^(3/2) +14sqrtx +C

Explanation:

Let u = x

int (u^2+3u +7)/sqrt(u)

Make it easier by simplifying integrals

int u^2/sqrt(u) + int (3u)/sqrtu + int 7/sqrt(u)

Simplify

int u^(3/2) + int 3sqrtu + int 7u^(-1/2)

Integrate

2/5*u^(5/2) + 3*(2/3)u^(3/2) + 7*2sqrtu

Sub back in x

(2/5)x^(5/2) +2x^(3/2) +14sqrtx +C