Question

Use substitution to find the indefinite integral

Answer 1

\[\int\limits_{?}^{?} \sqrt{5x+1} dx\]

Answer 2

Let \(u = 5x+1, ~du = 5dx \Rightarrow \dfrac{du}{5} = dx\)

Answer 3

\[\cdots~~~=\dfrac{1}{5}\int\sqrt{u}~du\]

Answer 4

Is this clear?

Answer 5

Yes, thank you

Answer 6

Glad I helped.

Answer 7

So how would I start \[\int\limits 2\cos(2x) dx\]

Answer 8

Let \(\displaystyle u = 2x, ~du = 2dx \Rightarrow\int2\cos(2x)dx = \int\cos(u)du\)