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Popular >

integral of xln(8)

Solution

integral

x ln (8)

Solution

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

Solution steps

\int x ln (8) d x

Take the constant out:

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

= ln (8) \cdot \int x d x

ln (8) = 3 ln (2)

= 3 ln (2) \cdot \int x d x

Apply the Power Rule

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

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

Simplify

3 ln (2) \frac{x ^{2}}{2} : \frac{3}{2} ln (2) x^{2}

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

Add a constant to the solution

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

Popular Examples

integral of (4x^2+x+5)/((x+1)(x^2+1))

\int \frac{4 x ^{2} + x + 5}{( x + 1 ) ( x ^{2} + 1 )} d x

integral of (8x^5-3x^2-2x+5)

\int (8 x^{5} - 3 x^{2} - 2 x + 5) d x

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

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

integral of 1/((2x+3)(x-1))

\int \frac{1}{( 2 x + 3 ) ( x - 1 )} d x

integral of (x+4)/(x^2+4x-12)

\int \frac{x + 4}{x ^{2} + 4 x - 12} d x

Frequently Asked Questions (FAQ)

What is the integral of xln(8) ?
The integral of xln(8) is 3/2 ln(2)x^2+C