Integration by parts

Exercise

1.

Find the following integral．

(a)

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

(b)

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

(c)

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

(d)

$${\int{x(x+5)^{14}}\ dx}$$

(e)

$${\int{x\cos{x}}\ dx}$$

(f)

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

(g)

$${\int{\log{(1+x^2)}}\ dx}$$

(h)

$${\int{x\tan^{-1}{x}}\ dx}$$

(i)

$${\int{x^n\log{x}}\ dx}$$ (n is integer)

(j)

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

(k)

$${\int{x\sinh{x}}\ dx}$$