Question

这2道大一的不定积分题怎么做?∫(arctg e^x)/ e^x dx ∫cos^5(x)/sin^4(x) dx

Answer 1

1、

首先de^x/dx=e^x

所以

原式=∫(arctg e^x)de^x

=1/(1+e^2x)+c

2、

原式=∫cos^4(x)/sin^4(x) dsinx

=∫[1-sin^2(x)]^2/sin^4(x) dsinx

=∫[1-2sin^2(x)+sin^4(x)]/sin^4(x) dsinx

=∫1/sin^4(x) dsinx-2∫1/sin^2(x)dsinx+∫1dsinx

=sinx+2/sinx-1/3sin^3(x)+c