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

Compute $\displaystyle \int\bigl(e^{-3x}+\cos(4x+5)-2\bigr)\,dx$

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

Compute $\displaystyle \int e^{3x+1} \, dx$

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

Find $\displaystyle \int (e^{3x+2}-4x+7) \, dx$

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

Compute the indefinite integral $\int \left( \sin(4x+5) - \frac{1}{2}x - 1 + e^{3x} \right) dx$.

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

Compute $\displaystyle \int\bigl(e^{3x}-\tfrac{3}{2}x+\cos(4x+5)\bigr)\,dx$.

Compute $\displaystyle \int (3\sin(4x+5) + 2e^{3x} - 5) \, dx$

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

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

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