IB Mathematics Analysis and Approaches Question Type 5: Integration by Parts in a Cycle Exercises

Find $$\int e^{2x}\sin (3x)dx$$

Evaluate the definite integral $${\int }_0^{\pi }{e}^x\sin xdx.$$

Find $\int e^{2x}\cos (3x)dx$.

Compute $$\int x{e}^x\sin xdx$$

Find $$\int e^{-x}\sin (2x)dx.$$

Compute $\int x{e}^x\cos xdx$.

Compute $$\int e^x\cos xdx.$$

Compute $$\int e^x\sin xdx.$$

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

Evaluate the definite integral $${\int }_0^{\frac{\pi }{2}}{e}^x\cos xdx.$$