Calculus II - Integration

 $\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx$  

•  $2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$  

•  $5x^{\frac{1}{3}}+4e^{-4x}+\ln\left|x\right|+C$  

•  $2x^{\frac{5}{2}}-4e^{-4x}+\ln\left|x\right|+C$  

• Nothing is correct

Solve $\int_{ }^{ }2\sin\left(\frac{x}{5}\right)dx$  

•  $\cos\left(\frac{x}{5}\right)+C$  

•  $-\frac{2}{5}\cos\left(\frac{x}{5}\right)+C$  

•  $-10\cos\left(\frac{x}{5}\right)+C$  

•  $-2\cos\left(5x\right)+C$  

Evaluate the indefinite integral using integration by parts. u and dv are provided.
 $\int t\sin t\ dt\ ;\ \ \ u=t,\ dv=\sin t\ dt$  

•  $t\cos^{-1}t-\left(1-t^2\right)^{\frac{1}{2}}+C$  

•  $-t\cos t+\sin t+C$  

•  $t\sin^{-1}t+\left(1-t^2\right)^{\frac{1}{2}}+C$  

•  $t\sin t+\cos t+C$  

Evaluate the indefinite integral using integration by parts. 
 $\int3x\ e^{2x}\ dx\$  

•  $-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C$  

•  $\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C$  

•  $xe^{-2x}+\frac{\left(1-x^2\right)^{ }}{2}+C$  

•  $-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C$