What is the integral of xln^2(x ?

The integral of xln^2(x is (x^3ln^2(d))/3+C

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integral of xln^2(x

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

\frac{x ^{3} ln ^{2} ( d )}{3} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= ln^{2} (d) \cdot \int xx d x

Simplify

xx : x^{2}

= ln^{2} (d) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= ln^{2} (d) \frac{x ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{3} ln ^{2} ( d )}{3}

Add a constant to the solution

= \frac{x ^{3} ln ^{2} ( d )}{3} + C

\frac{d}{d x} (arccot (x^{2}))

\frac{d}{d x} (3 e^{- 5 x})

f (x) = x^{3} - 12 x^{2} + 45 x

\int \frac{x ^{2}}{2 x - 1} d x

\int x (4 - x) d x