Question

Evaluate the integral by using multiple substitutions
∫5(3x^2-7)sin^5(x^3-7x) cos(x^3-7x) dx

Answer 1

\[\int\limits 5(3x^2-7)\sin^5(x^3-7x)\cos(x^3-7x)dx\]

Answer 2

u= x^3−7x
du = 3x^2-7 dx

Answer 3

well \[u=x^3-7x;du=3x^2-7\]
this leaves \[\int5sin^5(u)cos(u)du\]

Answer 4

v =sin (u)
dv = cos(u) du

Answer 5

so the answer would be \[5sin^6(x^3-7x)\]

Answer 6

Makes sense... THANK YOU BOTH!! ^_^

Answer 7

T.T i thought i could give both of u medals T.T