Integral of -5x^3-2x^2

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

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Answer

$-\frac{2}{3}x^{3}-\frac{5}{4}x^{4}+C_0$

Step by step solution

Problem

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

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

$\int-2x^2dx+\int-5x^3dx$
2

Taking the constant out of the integral

$\int-5x^3dx-2\int x^2dx$
3

Taking the constant out of the integral

$-5\int x^3dx-2\int x^2dx$
4

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

$-5\int x^3dx-2\frac{x^{3}}{3}$
5

Simplify the fraction

$-5\int x^3dx-\frac{2}{3}x^{3}$
6

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

$-5\frac{x^{4}}{4}-\frac{2}{3}x^{3}$
7

Simplify the fraction

$-\frac{5}{4}x^{4}-\frac{2}{3}x^{3}$
8

Add the constant of integration

$-\frac{2}{3}x^{3}-\frac{5}{4}x^{4}+C_0$

Answer

$-\frac{2}{3}x^{3}-\frac{5}{4}x^{4}+C_0$

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Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.21 seconds

Views:

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