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

Evaluate the definite integral $\displaystyle \int_{0}^{\frac{\pi}{4}} \cos(4x)\,dx$.

Find the indefinite integral $\displaystyle \int \sin(x)\,dx$.

Find the indefinite integral $\displaystyle \int \sin(5x)\,dx$.

Compute the indefinite integral $\displaystyle \int \bigl(5\cos(x) - 7\sin(x) + \tfrac{4}{x}\bigr)\,dx$.

Compute the indefinite integral $\displaystyle \int \bigl(6\sin(3x) - 9\cos(3x)\bigr)\,dx$.

Evaluate the definite integral $\displaystyle \int_{0}^{\frac{\pi}{2}} (2\sin x + 3\cos x)\,dx$.

Compute the indefinite integral $\displaystyle \int \left(10\sin(x) - \frac{2}{x} + 5\cos(x)\right)\,dx$.

Find the indefinite integral $\displaystyle \int \bigl(3\sin(2x) - 4\cos(2x)\bigr)\,dx$.

Evaluate the indefinite integral $\displaystyle \int \bigl(3\sin(x) + \cos(x) - \tfrac{2}{x}\bigr)\,dx$.

Find the indefinite integral $\displaystyle \int \left(3\cos(2x) + \frac{1}{x} - 2\sin(2x)\right)\,dx$.

Evaluate the definite integral $\displaystyle \int_{1}^{e} \left(\sin(x) + \frac{1}{x}\right)\,dx$.

Evaluate the definite integral $\displaystyle \int_{1}^{2} \left(2\cos(x) - \frac{1}{x}\right)\,dx$.