1/（x^4-1）的不定积分

解答过程如下：

∫1/(x^4-1)dx

=∫1/[(x?-1)(x?+1)]dx

=(1/2)∫[1/(x?-1)]-[1/(x?+1)]dx

=(1/2)∫[1/(x?-1)]dx-(1/2)∫[1/(x?+1)]dx

=(1/4)∫[1/(x-1)]-[1/(x+1)]dx-(1/2)arctanx

=(1/4)∫[1/(x-1)]dx-(1/4)∫[1/(x+1)]dx-(1/2)arctanx

=(1/4)ln|x-1|-(1/4)ln|x+1|-(1/2)arctanx

=(1/4)ln(|x-1|/|x+1|)-(1/2)arctanx

扩展资料

常用积分公式：

1）∫0dx=c

2）∫x^udx=(x^(u+1))/(u+1)+c

3）∫1/xdx=ln|x|+c

4）∫a^xdx=(a^x)/lna+c

5）∫e^xdx=e^x+c

6）∫sinxdx=-cosx+c

7）∫cosxdx=sinx+c