Choose which expression is u

Question

In using the technique of integration by parts, you must carefully choose which expression is u . For the following problem, use the guidelines in this section to choose u . Do not evaluate the integral.

∫x^4cos(5x)dx

Answer 1

choosing x⁴=u, then du=4x³

then the integral = (x⁴)(sin(5x)/5 -∫(4/5)x³(sin(5x))dx = u*v-∫v*du

now choose x³=u so du=3u² applied to remaining integral

continue until x=u so du=dx