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Integration C3

Ive been stuck on this for a bit now :

Show Integral between 3 and 0 x + 1 / x(squared) + 9 = 0.5 ln2 + pi/12

thanx in advance...
Reply 1
Avatar for SCE1912
SCE1912
Here's a hint, Split the numerator to give
∫03xx2+9+1x2+9dx\displaystyle \int^3_0 \frac{x}{x^2+9} + \frac{1}{x^2+9} dx
Reply 2
Avatar for Dadeyemi
Dadeyemi
13
(x+1)/(x^2+9) ?

int: (x+1)/(x^2+9)dx = int[x/(x^2+9) + 1/(x^2+9)]dx

substitute x=3u

the result should be easy enough to integrate

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