Question

How do I integrate the following using the by parts technique: x(X+1)^0.5

Answer 1

\[\int\limits {x\sqrt {x+1}dx}\]

Answer 2

Why do you need use integration by parts here?

Answer 3

Thats what the question asks for...

Answer 4

\[\int\limits x \sqrt{x + 1} dx = \int\limits x\left(x + 1\right)^{\frac{1}{2}}dx\]\[u = x\]\[du = dx\]\[dv = \left( x + 1 \right)^{\frac{1}{2}}dx\]\[v = \frac{2}{3}\left( x + 1 \right)^{\frac{3}{2}}\]\[\int\limits u dv = uv - \int\limits v du\]\[\int\limits x \left( x + 1 \right)^{\frac{1}{2}} dx = \frac{2}{3}x \left( x + 1 \right)^{\frac{3}{2}}- \int\limits \frac{2}{3}\left( x + 1 \right)^{\frac{1}{2}}dx\]continue to integrate the right side

Answer 5

Thanks for that - much appreciated