Quick questions on Integrating exponential and trigonometric functions explained: O-Level A-Maths

Reverse the standard derivatives:

The same standard results apply to definite integrals: integrate first, then substitute the upper and lower limits and subtract. For exponentials and trigonometric functions this often produces neat exact values, such as $\int_0^{\pi} \sin x\,dx = [-\cos x]_0^{\pi} = 2$, which examiners expect to be left exact rather than rounded.

Since integration reverses differentiation, differentiate your answer to confirm it returns the integrand. This quickly exposes a dropped minus sign on a sine, a missing modulus on a logarithm, or a forgotten inner-coefficient division on a composite.

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

Find $\displaystyle\int \cos 2x\,dx$. [2 marks]

Find $\displaystyle\int \dfrac{5}{x}\,dx$. [2 marks]