Integration by Substitution (Part 1)
How to solve the integration by substitution problems (indefinite integration): examples and their solutions.
Set 2x - 1 = t.
Differentiate both sides:
2 dx = dt
dx = (1/2)dt.
Substitute [2x - 1] with [t].
And substitute [dx] with [(1/2)dt].
Then (given) = ∫ t8 (1/2)dt.
Put 2x - 1 in t.
Then (given) = (1/18)(2x - 1)9 + C.
Put sin x in t.
Then (given) = (1/6) sin6 x + C.