Integration by substitution

3x^2 cos(x^3+5)

i know the answer is sin(x^3+5)+C but i don't know how to get there with appropriate working.

thank you in advance

when using substitution, look for the variable with the highest power.

u=x^3+5
du=(3x^2)dx

So, now you have the integral of cos(u)du.

∫cos(u)du = sin(u)

Now substitute back in for u

sin(u)=sin(x^3+5)+C

∫ 3x^2 cos(x^3 + 5) dx

Let u = x^3 + 5
du = 3x^2 dx

So substitute in:

∫ cos(x^3 + 5) * 3x^2 dx
∫ cos(u) du

This would be:
sin(u) + C

Substitute back (u = x^3 + 5):

sin(x^3 + 5) + C

Let u = x^3 + 5

du = 3x^2 dx

∫ cos(u) du

sin(u) + C

Back substitute:
sin(x^3+5) + C

∫3x^2 cos(x^3 + 5) dx => u = x^3 + 5

du = 3x^2 dx

∫cos(u) du = sin(u) + C = sin(x^3 + 5) + C