Calculus • Step-by-Step

Integral of (2x + 3) dx with Steps

Integrate the linear binomial (2x + 3) term by term. Shows step-by-step working resulting in x² + 3x + C.

Problem Statement

\int (2x + 3) \, dx

Final Result

F(x) = x^{2}+3 \cdot x + C

Formula Required: Sum Rule for Integration

Integrate 2x to x² and 3 to 3x, then add the constant C.

\int (ax + b) \, dx = \frac{a x^2}{2} + bx + C

5 Steps

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

\int \left( 2 \cdot x+3 \right) \, dx

Apply the Sum & Difference Rule: integrate each term separately.

\int \left( 2 \cdot x+3 \right) \, dx = \int 2 \cdot x \, dx + \int 3 \, dx

Integrate term $2 \cdot x$ using the Power Rule for integration.

\int 2 \cdot x \, dx = x^{2}

Integrate constant $3$ to obtain $3 \cdot x$.

\int 3 \, dx = 3 \cdot x

Combine all term antiderivatives.

F(x) = x^{2}+3 \cdot x

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

∫ 2x dx + ∫ 3 dx = 2(x²/2) + 3x = x² + 3x + C.