t

3t

e^2t

e^t

don't use IBP, let u = 2t

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

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

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

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

 $\frac{2t^2\ln2t-t^2}{4}+C$  

 $\frac{t^3\ \ln3}{3}-\frac{t^3}{9}+C$  

 $\frac{e^t}{2t+2}+C$  

 $\frac{-2t-1}{4e^{2t}}+C$  

 $\frac{e^x}{4x+4}+C$  

 $\frac{2x^{\frac{3}{2}}\ln4x}{3}-\frac{4x^{\frac{3}{2}}}{9}+C$  

 $\frac{\left(4x^2-1\right)\cdot e^{4x^2}}{32}+C$  

 $\frac{x^5\ln x}{5}-\frac{x^5}{25}+C$  

 $xe^x-\ e^x+c$  

 $xe^x+e^x+c$  

 $xe^x+c$  

 $xe^x-e^x$  

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

 $-t\cos t+\sin t+C$  

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

 $t\sin t+\cos t+C$  

x

sin(x)

cos(x)

e^x

antiderivative rules.

u-substitution

integration by parts

Stare at the question... forever.