Integration by substitution

Exercise

1.

Find the following integral．

(a)

$${\int{e^{2-x}}\ dx}$$

(b)

$${\int{\sec^2{(1-x)}}\ dx}$$

(c)

$${\int{\frac{x}{\sqrt{1-x^2}}}\ dx}$$

(d)

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

(e)

$${\int{\frac{e^{1/x}}{x^2}} \ dx}$$

(f)

$${\int{\frac{\sec^2{\theta}}{\sqrt{3\tan{\theta} + 1}}}\ d\theta}$$

(g)

$${\int{\frac{1+\cos{2x}}{\sin^2{x}}} \ dx}$$

(h)

$${\int{\frac{\log{x}}{x}}\ dx }$$

(i)

$${\int{\frac{e^x}{1 + e^{2x}}} \ dx}$$

(j)

$${\int{x\sin{(x^2)}} \ dx}$$