Question

求几道简单的积分题

1.∫（4X-1）^1/2 dx
2.∫sin（a-bX）dx
3.∫dx/1-10X
4.∫x^2dx/(1+x^3)^1/3
5.∫e^(sinx)cosxdx
给个大致过程，谢谢

Answer 1

1. (1/6)*(4X - 1)^(3/2) + C

2. (1/b)*cos(a - bx) + C

3. (-1/10)*ln|1-10x| + C (P.S: | | 指的是绝对值符号)

4. using substitution 1+ x^3 = u^3
(3x^2)dx = (3u^3)du
∫(u)du = (1/2)*(u^2)+ C = (1/2)[(1+ x^3)^(2/3)] + C

5. (e^sinx) + C
Hint: put sinx = t