Integration by Parts State whether you would use integration by parts to evaluate each
Chapter 8, Problem 61(choose chapter or problem)
State whether you would use integration by parts to evaluate each integral. If so, identify what you would use for \(u\) and \(d v\). Explain your reasoning.
(a) \(\int \frac{\ln x}{x} d x\)
(b) \(\int x \ln x d x\)
(c) \(\int x^{2} e^{-3 x} d x\)
(d) \(\int 2 x e^{x^{2}} d x)
(e) \(\int \frac{x}{\sqrt{x+1}} d x\)
(f) \(\int \frac{x}{\sqrt{x^{2}+1}} d x\)
Text Transcription:
u
dv
int ln x / x dx
int x ln x dx
int x^{2} e^{-3x} dx
int 2x e^{x^2} dx
int x / sqrt{x + 1} dx
int x / sqrt{x^{2} + 1} dx
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