Question Type 5: Integration by parts in a cycle Bootcamps

Compute $\displaystyle \int e^x\cos x\,dx.$

Compute $\displaystyle \int e^x\sin x\,dx.$

Compute $\displaystyle \int e^{2x}\cos(3x)\,dx.$

Compute $\displaystyle \int e^{2x}\sin(3x)\,dx.$

Compute $\displaystyle \int e^{-x}\sin(2x)\,dx.$

Compute $\displaystyle \int e^{-x}\cos(2x)\,dx.$

Evaluate the definite integral $\displaystyle \int_{0}^{\frac{\pi}{2}}e^x\cos x\,dx.$

Evaluate the definite integral $\displaystyle \int_{0}^{\pi}e^x\sin x\,dx.$

Compute $\displaystyle \int x e^x\cos x\,dx.$

Compute $\displaystyle \int x e^x\sin x\,dx.$