# Integrate (x-1)^5+3(x-1)^2+5

## Answer

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

## Step-by-step explanation

Problem to solve:

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

1

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

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

## Answer

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