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# Integral of 3(x-1)^2+5+(x-1)^5

### Formulas

$5x+\left(1-2x+x^2\right)\left(x-1\right)+\frac{\left(x-1\right)^{6}}{6}+C_0$

## Step-by-step explanation

Problem

$\int\left(\left(x-1\right)^5+3\left(x-1\right)^2+5\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int5dx+\int3\left(x-1\right)^2dx+\int\left(x-1\right)^5dx$

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

### Main topic:

Integration by substitution

0.42 seconds