1. ## Integration by Substitution

Hi, I'm new to integration. Can anyone help me figure out where I went wrong?
Many thanks.

Q. Evaluate the following:

2. ## Re: Integration by Substitution

Notice your u version of the integrand has no traces of the x in the numerator of the original. To bring that part with you, you can re-express it (x, that is) in terms of u, or else use integration by parts.

3. ## Re: Integration by Substitution

Originally Posted by GrigOrig99
Hi, I'm new to integration. Can anyone help me figure out where I went wrong?
Many thanks.

Q. Evaluate the following:

Your numerator disappeared when changing the variable. Express x in terms of u.

edit: drat, beaten to it

4. ## Re: Integration by Substitution

You haven't taken into account the $x$ on the numerator.

We have:

$\int^4_0{\frac{x}{\sqrt{2x+1}}}dx$

I'm going to let $u^2=2x+1$ so that $2u~du=2~dx$ and $dx=u~du$

When $x=4$, $u=3$ and when $x=0$, $u=1$

I have:

$\int^4_0{\frac{x}{\sqrt{2x+1}}}dx$

= $\int^3_1{\frac{u^2-1}{2u}}\cdot{u}~du$

Take it!

5. ## Re: Integration by Substitution

The parts version...

... where (key in spoiler) ...

Spoiler:

... is the product rule, straight continuous lines differentiating downwards with respect to x.

... is lazy integration by parts, doing without u and v.

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Thanks guys.