Write Integral: Write down the integral to be solved. I = ∫3x^(-2)dxSimplify Integral: Simplify the integral. I = 3∫x^(-2)dxRecall Power Rule: Recall the power rule for integration, ∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1.Apply Power Rule: Apply the power rule to the integral. I = 3((x^(-2+1))/(-2+1)) + C I = 3((x^(-1))/(-1)) + CSimplify Expression: Simplify the expression. I = -3x^(-1) + C I = -3/x + CFinal Answer: Write the final answer. The indefinite integral of 3x^(-2) with respect to x is -3/x + C.

Calculus

Find indefinite integrals using the substitution and by parts

Full solution

\int 3x^{-2}\,dx

Write Integral: Write down the integral to be solved. $\newline$ $I = \int 3x^{-2}\,dx$
Simplify Integral: Simplify the integral. $I = 3\int x^{-2}\,dx$
Recall Power Rule: Recall the power rule for integration, $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ , where $n \neq -1$ .
Apply Power Rule: Apply the power rule to the integral. $\newline$ $I = 3\left(\frac{x^{(-2+1)}}{(-2+1)}\right) + C$ $\newline$ $I = 3\left(\frac{x^{(-1)}}{(-1)}\right) + C$
Simplify Expression: Simplify the expression. $\newline$ $I = -3x^{-1} + C$ $\newline$ $I = -\frac{3}{x} + C$
Final Answer: Write the final answer. $\newline$ The indefinite integral of $3x^{-2}$ with respect to $x$ is $-\frac{3}{x} + C$ .