Integrate 18x^2+4x

\int\left(18x^2+4x\right)dx

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Answer

$2x^2+6x^{3}+C_0$

Step by step solution

Problem

$\int\left(18x^2+4x\right)dx$
1

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

$\int4xdx+\int18x^2dx$
2

Taking the constant out of the integral

$4\int xdx+\int18x^2dx$
3

Taking the constant out of the integral

$4\int xdx+18\int x^2dx$
4

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

$4\int xdx+18\frac{x^{3}}{3}$
5

Simplify the fraction

$4\int xdx+6x^{3}$
6

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

$4\cdot \frac{1}{2}x^2+6x^{3}$
7

Multiply $\frac{1}{2}$ times $4$

$2x^2+6x^{3}$
8

Add the constant of integration

$2x^2+6x^{3}+C_0$

Answer

$2x^2+6x^{3}+C_0$

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Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.22 seconds

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