1. ## Need help with a integral please

I have this integral i need to solve, iv been thinking about dividing (x+1)^4 in (x+1)^2 * (x+1)^2 and then dividing the integral but i dont know if this is posible considering that it contains x^1/2 ...can anyone help me figure it out please?

2. ## Re: Need help with a integral please

Originally Posted by purpleclover
I have this integral i need to solve, iv been thinking about dividing (x+1)^4 in (x+1)^2 * (x+1)^2 and then dividing the integral but i dont know if this is posible considering that it contains x^1/2 ...can anyone help me figure it out please?
\displaystyle \begin{align*} \int{\frac{1}{\sqrt{x}(x + 1)^4}\,dx} = 2\int{\frac{1}{(x + 1)^4}\,\frac{1}{2\sqrt{x}}\,dx} \end{align*}

Make the substitution \displaystyle \begin{align*} u = \sqrt{x} \implies du = \frac{1}{2\sqrt{x}}\,dx \end{align*} and the integral becomes \displaystyle \begin{align*} 2\int{\frac{1}{\left(u^2 + 1\right)^4}\,du} \end{align*}.

Then make the substitution \displaystyle \begin{align*} u = \tan{\theta} \implies du = \sec^2{\theta}\,d\theta \end{align*}

Thanks alot!