Question Type 2: Applying integration through using the basis integrals alongside their composite transformations in linear functions Exercises

Compute $\displaystyle\int\bigl(x\sin(4x+5)+x e^{3x}\bigr)dx$.

Find $\displaystyle\int x^2 e^{3x}\,dx$.

Find $\displaystyle\int\left(\sin(4x+5)-\frac{1}{2}x-1+e^{3x}\right)\,dx$.

Find $\displaystyle\int\left(3\sin(4x+5)+2e^{3x}-\frac{x}{2}\right)\,dx$.

Compute $\displaystyle\int -\frac{1}{2}x\,dx$.

Find $\displaystyle\int x^2\sin(4x+5)\,\text{d}x$.

Find $\displaystyle\int e^{3x}\,dx$.

Find $\displaystyle\int e^{3x}\sin(4x+5)\,dx$.

Compute $\displaystyle\int \sin(4x+5)\,dx$.

Find $\displaystyle\int x\sin(4x+5)\,dx$.

Find $\displaystyle\int x e^{3x}\,dx$.

Compute $\displaystyle\int -1\,dx$.