# Determine the following indefinite integral. \int (x^{8}-3x^{3}+1)dx

Determine the following indefinite integral.
$\int \left({x}^{8}-3{x}^{3}+1\right)dx$
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Richard Cheatham
Step 1
First we separate the integral.
$\int \left({x}^{8}-3{x}^{3}+1\right)dx$
$=\int {x}^{8}dx-3\int {x}^{3}dx+\int dx$
Step 2
Then we integrate each part
$\int \left({x}^{8}-3{x}^{3}+1\right)dx$
$=\int {x}^{8}dx-3\int {x}^{3}dx+\int dx$
$=\frac{{x}^{9}}{9}-3\frac{{x}^{4}}{4}+x+C$
$=\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x+C$
Answer: $\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x+C$
C=integrating constant
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Xyle1991
Step 1: Expand.
$\int \left({x}^{8}-3{x}^{3}+1\right)dx$
Step 2: Use Power Rule: $\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$.
$\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x$
$\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x+C$