Calculus • Step-by-Step

Integral of (3x + 5) dx with Steps

Step-by-step antiderivative of (3x + 5) dx. Integrates each linear and constant term individually to find the solution (3/2)x² + 5x + C with steps.

Problem Statement

\int (3x + 5) \, dx

Final Result

F(x) = \frac{3 \cdot x^{2}}{2}+5 \cdot x + C

Formula Required: Linear Term Integration

Use power rule on 3x (gives 3x²/2) and constant rule on 5 (gives 5x).

\int (3x + 5) \, dx = \frac{3}{2}x^2 + 5x + C

5 Steps

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

\int \left( 3 \cdot x+5 \right) \, dx

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

\int \left( 3 \cdot x+5 \right) \, dx = \int 3 \cdot x \, dx + \int 5 \, dx

Integrate term $3 \cdot x$ using the Power Rule for integration.

\int 3 \cdot x \, dx = \frac{3 \cdot x^{2}}{2}

Integrate constant $5$ to obtain $5 \cdot x$.

\int 5 \, dx = 5 \cdot x

Combine all term antiderivatives.

F(x) = \frac{3 \cdot x^{2}}{2}+5 \cdot x

Interactive Calculator

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

∫ 3x dx + ∫ 5 dx = 3(x²/2) + 5x + C = (3/2)x² + 5x + C.