What is the integral of x^{19}Inx ?

The integral of x^{19}Inx is (Inx^{21})/(21)+C

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integral of x^{19}Inx

\int x^{19} I n x d x

\frac{I n x ^{21}}{21} + C

Solution steps

\int x^{19} 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^{19} d x

Simplify

x x^{19} : x^{20}

= I n \cdot \int x^{20} d x

Apply the Power Rule

: \frac{x ^{21}}{21}

= I n \frac{x ^{21}}{21}

Multiply fractions:

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

= \frac{I n x ^{21}}{21}

Add a constant to the solution

= \frac{I n x ^{21}}{21} + C

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What is the integral of x^{19}Inx ?
The integral of x^{19}Inx is (Inx^{21})/(21)+C