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Step-by-step Solution

Integrate (1-x)^30

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Answer

$-\frac{1}{31}\left(1-x\right)^{31}+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(1-x\right)^{30}dx$
1

Solve the integral $\int\left(1-x\right)^{30}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=1-x \\ du=-1dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{-1}=dx$

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Answer

$-\frac{1}{31}\left(1-x\right)^{31}+C_0$
$\int\left(1-x\right)^{30}dx$

Main topic:

Integration by substitution

Used formulas:

6. See formulas

Time to solve it:

~ 0.44 seconds