Use integration by parts to evaluate integral: int[0,3] ln(x^2+9) dx

[blue27]

Use integration by parts to evaluate this integral:

. . . . .\(\displaystyle \displaystyle \int_0^3\, \ln(x^2\, +\, 9)\, dx\)

 

[tkhunny]

Use integration by parts to evaluate this integral:

. . . . .\(\displaystyle \displaystyle \int_0^3\, \ln(x^2\, +\, 9)\, dx\)

Okay, what have you tried? Perhaps the basic formulation?

Here's the Indefinite Version

\(\displaystyle \int\ln\left(x^{2}+9\right)\;dx = x\cdot\ln\left(x^{2}+9\right)-\int\;x\;d\left[\ln\left(x^{2}+9\right)\right]\)

Where do we go from there?