Question

integrate sin5x dx

Answer 1

sin differentiates to cosine so
sin integrates to -cos(x)
make up for the 5 with 1/5
so
-1/5cos(5x)

Answer 2

take 5x=t
then the integral transforms to S 1/5 sint dt
1/5 is constant and integral of sint is -cost
Therefore your answer will be
-1/5cos(t)
Substitute back for t and you get your answer as
-1/5sin(5x)+constant

Answer 3

Unless you mean \(\int \sin^5x~dx~?\)

Answer 4

hope not lol