Question

A solucao de $\int{\sqrt{6ax}\, dx$ está apresentada em:

Answer 1

$\int \left(\sqrt{6ax}\right)dx\\\int \left(\sqrt{6a}\cdot \sqrt{x}\right)dx\\\sqrt{6a}\cdot \int \left(\sqrt{x}\right)dx\\\sqrt{6a}\cdot \int \left(x^{\frac{1}{2}}\right)dx\\\sqrt{6a}\cdot \frac{2x^{\frac{3}{2}}}{3}+c\\\sqrt{6a}\cdot \frac{3x\sqrt{x}}{2}+c\\\boxed{\bold{\frac{3x\sqrt{6ax}}{2}+c}}$

Answer 2

$\displaystyle\sf{\int\sqrt{6ax}~dx=\sqrt{6a}\int x^{\frac{1}{2}}dx}\\\sf{\dfrac{2\sqrt{6a}}{3}x^{\frac{3}{2}}+k}$