Question Type 1: Applying integration through using the basis integrals Exercises

Evaluate the integral

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

Evaluate the indefinite integral $\int \left(3\sin x + \cos x - \frac{2}{x}\right) \mathrm{d}x$

Find $\int\sin(5x-2)\,dx$.

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

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

Find $\int \left( 2\cos \left( 3x + \frac{\pi}{4} \right) + \frac{1}{x} \right) dx$.

Evaluate $\displaystyle\int\left(e^{2x+1} - \frac{3}{x}\right) \, \text{d}x$.

Evaluate $\int (5e^{-2x} + 4\cos(3x)) \, dx$.

Evaluate $\displaystyle\int\bigl(e^{-\frac{x}{2}} - 4\sin(2x)\bigr)\,dx$.

Find $\displaystyle\int\cos(2x-3)\,dx$.

Find $\displaystyle\int \left( -\frac{3}{x} + \sin(7x) + e^x \right) dx$.