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Popular >

integral of xln(3)

Solution

\int x ln (3) d x

Solution

\frac{1}{2} ln (3) x^{2} + C

Solution steps

\int x ln (3) d x

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

ln (3) \frac{x ^{2}}{2} : \frac{1}{2} ln (3) x^{2}

= \frac{1}{2} ln (3) x^{2}

Add a constant to the solution

= \frac{1}{2} ln (3) x^{2} + C

Popular Examples

limit as x approaches 1+of (2-x)/(x-1)

x \to 1 + lim (\frac{2 - x}{x - 1})

y^{''}-12y^'+36y=4xe^{6x}

y^{^{''}} - 12 y^{^{'}} + 36 y = 4 x e^{6 x}

sum from n=2 to infinity of e^{3-2n}

n = 2 \sum \infty e^{3 - 2 n}

integral of 3(3x+9)^3

\int 3 (3 x + 9)^{3} d x

limit as x approaches 0 of (sinh(x)-x)/(x^3)

x \to 0 lim (\frac{sinh ( x ) - x}{x ^{3}})

Frequently Asked Questions (FAQ)

What is the integral of xln(3) ?
The integral of xln(3) is 1/2 ln(3)x^2+C