What is the integral of (sqrt(x))^2 ?

The integral of (sqrt(x))^2 is (x^2)/2+C

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integral of (sqrt(x))^2

\int (x)^{2} d x

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

Solution steps

\int (x)^{2} d x

Simplify

(x)^{2} : x

= \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{2}}{2} + C

\int \frac{1}{x ln ( x ) ( ln ( ln ( x ) ) ) ^{2}} d x

(1 + x^{2} + y^{2} + x^{2} y^{2}) d y = (1 + y^{2}) d x

\int \frac{100}{100 - y} d y

y^{^{'''}} + 4 \cdot y^{^{'}} = 3 x - 1

x \to 1 lim (e^{4 x^{5} - 4 x})