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Popular >

integral of x^3In(x)

Solution

\int x^{3} I n (x) d x

Solution

\frac{I n x ^{5}}{5} + C

Solution steps

\int x^{3} I n x d x

Take the constant out:

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

= I n \cdot \int x x^{3} d x

Simplify

x x^{3} : x^{4}

= I n \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= I n \frac{x ^{5}}{5}

Multiply fractions:

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

= \frac{I n x ^{5}}{5}

Add a constant to the solution

= \frac{I n x ^{5}}{5} + C

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y^{2} = x^{3}, y^{2} = x

integral of (-9x^2+2)/(x^3+9x)

\int \frac{- 9 x ^{2} + 2}{x ^{3} + 9 x} d x

Frequently Asked Questions (FAQ)

What is the integral of x^3In(x) ?
The integral of x^3In(x) is (Inx^5)/5+C