What is the integral of 4xln(x^{11}) ?

The integral of 4xln(x^{11}) is 22x^2ln(x)-11x^2+C

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integral of 4xln(x^{11})

\int 4 x ln (x^{11}) d x

22 x^{2} ln (x) - 11 x^{2} + C

Solution steps

\int 4 x ln (x^{11}) d x

Take the constant out:

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

= 4 \cdot \int x ln (x^{11}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (x^{11}) - \int \frac{11 x}{2} d x

= 4 (\frac{1}{2} x^{2} ln (x^{11}) - \int \frac{11 x}{2} d x)

\int \frac{11 x}{2} d x = \frac{11 x ^{2}}{4}

= 4 (\frac{1}{2} x^{2} ln (x^{11}) - \frac{11 x ^{2}}{4})

Simplify

4 (\frac{1}{2} x^{2} ln (x^{11}) - \frac{11 x ^{2}}{4}) : 22 x^{2} ln (x) - 11 x^{2}

= 22 x^{2} ln (x) - 11 x^{2}

Add a constant to the solution

= 22 x^{2} ln (x) - 11 x^{2} + C

(- 7, - 2), (- 6, 7)

\frac{d}{d x} (\frac{( x + 2 ) ( 2 x + 4 )}{- x ^{2} - x - 2})

r^{2} - 15 x^{2}

lo g_{7} (x e^{x})

\frac{d}{d x} (\frac{7 x}{x ^{2} + 5})

What is the integral of 4xln(x^{11}) ?
The integral of 4xln(x^{11}) is 22x^2ln(x)-11x^2+C