# How do i solve this integral problem?

• May 12th 2009, 06:17 PM
da_coolest
How do i solve this integral problem?

Find and simplify te derivitive of

f(x) = (x²+2) log e(x²+2)

hence evaluate,

2
∫ x log e(x² + 2) dx
1

(note: that is "log to the base e" in everywhere that the "e" is mentioned )

• May 12th 2009, 06:22 PM
derfleurer
log of base e is just ln?
• May 13th 2009, 06:25 AM
HallsofIvy
Quote:

Originally Posted by da_coolest

Find and simplify te derivitive of

f(x) = (x²+2) log e(x²+2)

hence evaluate,

2
∫ x log e(x² + 2) dx
1

(note: that is "log to the base e" in everywhere that the "e" is mentioned )

Product rule. $f'= 2x log(x^2+ 2)+ (x^2+ 2)\frac{1}{x^2+2}(2x)$ $= 2x log(x^2+ 2)+ 2x$
$2\int x log(x^2+ 2)dx+ 2\log x dx= (x^2+2)log(x^2+ 2)+ C$