to evaluate the indefinite integral of 3x2 with respect to x.

April 9, 2026Mathematics

ScanSolve AI Answer

April 9, 2026

Answer

$x^3 + C$

Step 1: Identify the integral. The problem asks to evaluate the indefinite integral of $3x^2$ with respect to $x$ . $\int 3x^2 dx$

Step 2: Apply the constant multiple rule for integration. The constant multiple rule states that $\int c \cdot f(x) dx = c \int f(x) dx$ . Here, $c=3$ and $f(x)=x^2$ . $\int 3x^2 dx = 3 \int x^2 dx$

Step 3: Apply the power rule for integration. The power rule for integration states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ , where $n \neq -1$ . Here, $n=2$ . $3 \int x^2 dx = 3 \left( \frac{x^{2+1}}{2+1} \right) + C$ $= 3 \left( \frac{x^3}{3} \right) + C$

Step 4: Simplify the expression. $= \frac{3x^3}{3} + C$ $= x^3 + C$

The final answer is $\boxed{x^3 + C}$ .

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Quick Answer

The problem asks to evaluate the indefinite integral of 3x^2 with respect to x.
3x^2 dx Step 2: Apply the constant multiple rule for integration.
The constant multiple rule states that c · f(x) dx = c f(x) dx.
Here, c=3 and f(x)=x^2.

Asked on April 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 9, 2026

Step 1: Identify the integral. The problem asks to evaluate the indefinite integral of 3x^2 with respect to x. 3x^2 dx Step 2: Apply the constant multiple rule for integration. The constant multiple rule states that c · f(x) dx = c f(x) dx. Here, c=3 and f(x)=x^2. 3x^2 dx = 3 x^2 dx Step 3: Apply the power rule for integration. The power rule for integration states that x^n dx = x^n+1n+1 + C, where n ≠ -1. Here, n=2. 3 x^2 dx = 3 ( x^2+12+1 ) + C = 3 ( (x^3)/(3) ) + C Step 4: Simplify the expression. = (3x^3)/(3) + C = x^3 + C The final answer is x^3 + C.

Asked on April 9, 2026Mathematics

ScanSolve AI AnswerAnswered on April 9, 2026

Step 1: Identify the integral. The problem asks to evaluate the indefinite integral of 3x^2 with respect to x. 3x^2 dx Step 2: Apply the constant multiple rule for integration. The constant multiple rule states that c · f(x) dx = c f(x) dx. Here, c=3 and f(x)=x^2. 3x^2 dx = 3 x^2 dx Step 3: Apply the power rule for integration. The power rule for integration states that x^n dx = x^n+1n+1 + C, where n ≠ -1. Here, n=2. 3 x^2 dx = 3 ( x^2+12+1 ) + C = 3 ( (x^3)/(3) ) + C Step 4: Simplify the expression. = (3x^3)/(3) + C = x^3 + C The final answer is x^3 + C.