Question

evaluate the indefinite integral (fraction)

Answer 1

\[\int\limits_{}^{}\frac{ x + 2 }{ \sqrt{x^2 + 4x} }\]

Answer 2

how do I break this up

Answer 3

Use a large saw

Answer 4

That usually works...

Answer 5

well use substitution

let

\[u = x^2 + 4x\]

then the derivative

\[\frac{du}{dx} = 2x + 4\]

so then

\[du = 2x +4 ~ dx\]

but you need

x + 2 dx

so

\[\frac{1}{2} du = x + 2~dx\]

now substitute and you have

\[\int\limits \frac{1}{\sqrt{u} \times \frac{1}{2}du} = \frac{1}{2} \int\limits \frac{1}{\sqrt{u}} du\]

now use index laws to rewrite it

hope it makes sense

Answer 6

^ that could work too