# How do i solve this integral problem?

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• May 12th 2009, 07:17 PM
da_coolest
How do i solve this integral problem?
Im totally confused about the following problem. please help me to solve it and explain. following is the complete question:

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 )

Thanks in advance!
• May 12th 2009, 07:22 PM
derfleurer
log of base e is just ln?
• May 13th 2009, 07:25 AM
HallsofIvy
Quote:

Originally Posted by da_coolest
Im totally confused about the following problem. please help me to solve it and explain. following is the complete question:

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 )

Thanks in advance!

Product rule. $f'= 2x log(x^2+ 2)+ (x^2+ 2)\frac{1}{x^2+2}(2x)$ $= 2x log(x^2+ 2)+ 2x$
Now you know, from the "Fundamental Theorem of Caclulus" that
$2\int x log(x^2+ 2)dx+ 2\log x dx= (x^2+2)log(x^2+ 2)+ C$