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Step-by-step Solution

Integral of (10-9x)^3

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Answer

$-\frac{1}{36}\left(10-9x\right)^{4}+C_0$

Step-by-step explanation

Problem to solve:

$\int_{ }^{ }\left(10-9x\right)^3dx$
1

Solve the integral $\int\left(10-9x\right)^3dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=10-9x \\ du=-9dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{-9}=dx$

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Answer

$-\frac{1}{36}\left(10-9x\right)^{4}+C_0$

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$\int_{ }^{ }\left(10-9x\right)^3dx$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.59 seconds