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# Integrate x^2(x+1)

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##  Final Answer

$\frac{x^{4}}{4}+\frac{x^{3}}{3}+C_0$

##  Step-by-step Solution 

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Math interpretation of the question

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

Learn how to solve integral calculus problems step by step online.

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

Learn how to solve integral calculus problems step by step online. Integrate x^2(x+1). Math interpretation of the question. Rewrite the integrand x^2\left(x+1\right) in expanded form. Expand the integral \int\left(x^{3}+x^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{3}dx results in: \frac{x^{4}}{4}.

##  Final Answer

$\frac{x^{4}}{4}+\frac{x^{3}}{3}+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of x^2(x+1)dx using partial fractionsSolve integral of x^2(x+1)dx using basic integralsSolve integral of x^2(x+1)dx using u-substitutionSolve integral of x^2(x+1)dx using integration by partsSolve integral of x^2(x+1)dx using trigonometric substitution

### Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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