Calculus • Step-by-Step

Integral of (x + 1)² dx with Steps

Step-by-step integration of (x + 1)². Expands into x² + 2x + 1 and integrates term-by-term to get x³/3 + x² + x + C.

Problem Statement
∫(x+1)2 dx\int (x + 1)^2 \, dx
Final Result
F(x)=x33+x2+x+CF(x) = \frac{x^{3}}{3}+x^{2}+x + C

Formula Required: Expansion & Power Rule

Expand the square binomial first, then integrate each term.

∫(x+1)2 dx=∫(x2+2x+1) dx=x33+x2+x+C\int (x+1)^2 \, dx = \int (x^2 + 2x + 1) \, dx = \frac{x^3}{3} + x^2 + x + C

Step-by-Step Solution

2 Steps
1

Set up the indefinite integral with respect to variable $x$.

∫((x+1)2) dx\int \left( \left(x+1\right)^{2} \right) \, dx
2

Apply the Power Rule for Integration to find the antiderivative.

F(x)=x33+x2+xF(x) = \frac{x^{3}}{3}+x^{2}+x

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Common Questions About Integral of (x + 1)² dx

How do you integrate (x+1)²?

Expand to x² + 2x + 1. Integrate term by term: x³/3 + x² + x + C.

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