• A Level Maths

Demo

• A Level
• Integration (exp/trig)

1. Find $$\displaystyle\int \dfrac{\cos x}{1+\sin x} \ \mathrm{d}x$$

$\ln|1+\sin x| +c$

2. Find $$\displaystyle\int \mathrm{e}^{\sin x} \cos x \ \mathrm{d}x$$

$\mathrm{e}^{\sin x} +c$

3. Find $$\displaystyle\int \dfrac{\sin x}{\cos^2x} \ \mathrm{d}x$$

$\dfrac{1}{\cos x} +c$

4. Find $$\displaystyle\int 2\cosec^2 x + \sin x \ \mathrm{d}x$$

$-2\cot x -\cos x +c$

5. Find $$\displaystyle\int \dfrac{1}{\cos^2(3x+1)} \ \mathrm{d}x$$

$\dfrac{1}{3}\tan(3x+1) +c$

6. Find $$\displaystyle\int (\sec x + \tan x)^2 \ \mathrm{d}x$$

$2\tan x + 2\sec x - x +c$

7. Find $$\displaystyle\int \sin2x\cos^4 2x \ \mathrm{d}x$$

$-\dfrac{1}{10}\cos^5 2x +c$

8. Find $$\displaystyle\int (\sin x + \cos x)^2 \ \mathrm{d}x$$

$x - \dfrac{1}{2}\cos2x +c$

9. Find $$\displaystyle\int \sec^2 2x\tan^3 2x \ \mathrm{d}x$$

$\dfrac{1}{8}\tan^4 2x +c$

10. Find $$\displaystyle\int \cos^3x\sin^2x \ \mathrm{d}x$$

$\dfrac{1}{3}\sin^3 x - \dfrac{1}{5}\sin^5x +c$

11. Find $$\displaystyle\int \sin2x\cos2x \ \mathrm{d}x$$

$-\dfrac{1}{8}\cos 4x +c$

12. Find $$\displaystyle\int \sin^2x \ \mathrm{d}x$$

$\dfrac{x}{2} - \dfrac{\sin 2x}{4} +c$