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Step-by-step Solution

Integrate $t\sqrt{t^2-4}$ with respect to x

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Answer

$\frac{1}{3}\sqrt{\left(t^2-4\right)^{3}}+C_0$

Step-by-step explanation

Problem to solve:

$\int t\sqrt{t^2-4}dt$
1

Solve the integral $\int t\sqrt{t^2-4}dt$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=t^2-4 \\ du=2tdt\end{matrix}$
2

Isolate $dt$ in the previous equation

$\frac{du}{2t}=dt$

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Answer

$\frac{1}{3}\sqrt{\left(t^2-4\right)^{3}}+C_0$
$\int t\sqrt{t^2-4}dt$

Main topic:

Integration by substitution

Used formulas:

3. See formulas

Time to solve it:

~ 0.82 seconds

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