Calculus 2

1. Use integration by parts to evaluate the indefinite integral

∫5𝑥sin(𝑥)𝑑𝑥.∫5xsin⁡(x)dx.

Answer:

2. Use integration by parts to evaluate the definite integral

∫60 𝑡𝑒^-t 𝑑𝑡.∫06te−tdt.

Answer:

3. Evaluate the integral 

∫4(ln 𝑥)^2 𝑑𝑥

Note: Use an upper-case "C" for the constant of integration.

4. Evaluate the integral 

∫𝑒^2𝑡 sin(3𝑡) 𝑑t

Note: Use an upper-case "C" for the constant of integration.

5. Find the integral

∫arctan(4𝑤)𝑑𝑤

6. Evaluate the definite integral.

∫31√t ln(𝑡)𝑑𝑡

7. Find the integral 

∫ 7𝑡^2 sin(𝑡)𝑑𝑡