State whether you would use integration by parts to evaluate each integral. If so

Chapter 8, Problem 78

(choose chapter or problem)

CAPSTONE

State whether you would use integration by parts to evaluate each integral. If so, identify what you would use for u and dv. 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:

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