Integration of trigonometric functions

Exercise

1.

Find the following integral．

(a)

$${\int{\sin^3{x}}\ dx}$$

(b)

$${\int{\sin^2{3x}}\ dx}$$

(c)

$${\int{\sin^3{x}\cos^2{x}}\ dx}$$

(d)

$${\int{\cos{3x}\sin{2x}} \ dx }$$

(e)

$${\int{\sin^5{x}}\ dx}$$

(f)

$${\int{\sec^2{\pi x}}\ dx}$$

(g)

$${\int{\tan^3{x}}\ dx}$$

(h)

$${\int{\tan^2{x}\sec^2{x}}\ dx}$$

(i)

$${\int{\tan^3{x}\sec^3{x}}\ dx}$$

(j)

$${\int{\sec^5{x}}\ dx}$$

(k)

$${\int{\frac{dx}{3 - 2\cos{x}}}}$$

(l)

$${\int{\frac{\sin{x}}{2 - \sin{x}}}\ dx}$$

(m)

$${\int{\frac{1 + \sin{x}}{1 + \cos{x}}}\ dx}$$

(n)

$${\int{\frac{\sin^2{x}}{\sin^2{x} - \cos^2{x}}}\ dx}$$

(o)

$${\int{\frac{dx}{1 + \tan{x}}}}$$