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Integral of (x^3)/((x-1)^0.5)

\int\frac{x^3}{\sqrt{x-1}}dx

Step by step solution

Problem

$\int\frac{x^3}{\sqrt{x-1}}dx$

Show full step-by-step solution

Answer

$2\left(\frac{6}{7}\left(\frac{4}{5}\left(\frac{2}{3}\sqrt{x-1}+\frac{1}{3}\cdot\frac{\sqrt{x-1}x^{3}}{x}\right)+\frac{1}{5}\cdot\frac{\sqrt{x-1}x^{5}}{x}\right)+\frac{1}{7}\cdot\frac{\sqrt{x-1}x^{7}}{x}\right)+C_0$
$\int\frac{x^3}{\sqrt{x-1}}dx$

Main topic:

Integration by trigonometric substitution

Used formulas:

4. See formulas

Time to solve it:

0.7 seconds