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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Integration by substitution

Used formulas:

7. See formulas

Time to solve it:

~ 0.7 seconds