Integrate x^4(2-1x^2)

\int x^4\left(2-x^2\right)dx

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Answer

$-\frac{x^{7}}{7}+\frac{2}{5}x^{5}+C_0$

Step by step solution

Problem

$\int x^4\left(2-x^2\right)dx$
1

Multiplying polynomials $x^4$ and $2+-x^2$

$\int\left(2x^4-x^{6}\right)dx$
2

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

$\int-x^{6}dx+\int2x^4dx$
3

Taking the constant out of the integral

$\int2x^4dx-\int x^{6}dx$
4

Taking the constant out of the integral

$2\int x^4dx-\int x^{6}dx$
5

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$2\int x^4dx-\frac{x^{7}}{7}$
6

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$2\frac{x^{5}}{5}-\frac{x^{7}}{7}$
7

Simplify the fraction

$\frac{2}{5}x^{5}-\frac{x^{7}}{7}$
8

Add the constant of integration

$-\frac{x^{7}}{7}+\frac{2}{5}x^{5}+C_0$

Answer

$-\frac{x^{7}}{7}+\frac{2}{5}x^{5}+C_0$

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Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.28 seconds

Views:

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