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

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

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

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

Compute $\displaystyle \int\bigl(4x-\tfrac{1}{2}+e^{3x}\bigr)\,dx$

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

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

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

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

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

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

Compute $\displaystyle \int \bigl(\sin(4x+5) - \tfrac{1}{2}x - 1 + e^{3x}\bigr)\,dx$

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

Compute $\displaystyle \int\bigl(2e^{3x}+\sin(2x+1)-\tfrac{5x}{2}-3\bigr)\,dx$