We read your photo as:

Evaluate ∫(1/x^(1/2))dx

July 1, 2026Mathematics

ScanSolve AI Answer

Answer

-\frac{1}{x} - x^2 + C

3 steps

Rewrite the integrand using negative exponents.
The term $\frac{1}{x^2}$ can be written as $x^{-2}$ .
$\int \left( \frac{1}{x^2} - 2x \right) dx = \int (x^{-2} - 2x^1) dx$
Apply the power rule for integration, which states $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ for $n \neq -1$ .
Integrate each term of the expression:
For the first term, $x^{-2}$ :
$\int x^{-2} dx = \frac{x^{-2+1}}{-2+1} = \frac{x^{-1}}{-1} = -\frac{1}{x}$
For the second term, $-2x^1$ :
$\int -2x^1 dx = -2 \frac{x^{1+1}}{1+1} = -2 \frac{x^2}{2} = -x^2$
Combine the results of the integration and add the constant of integration, $C$ .
$\int \left( \frac{1}{x^2} - 2x \right) dx = -\frac{1}{x} - x^2 + C$
The evaluated integral is $-\frac{1}{x} - x^2 + C$ .