Question

What is the integral of `10sin(x/5)`?

Answer 1

It is `-50cos(x/5)`

`int 10 sin(x/5) dx = 10 intsin(x/5) dx`

Let `u = x/5` so that `du = 1/5 dx` and therefore `dx = 5 du`

Substitute:

`10 int sin(x/5) dx = 10 int (sinu) 5 du = 50 int sinu du`

Now integrate:

#10 int sin(x/5) dx = 50 (-cos u) +C
And finally, reverse the substitution:

`10 int sin(x/5) dx = -50 cos (x/5)+C`