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Popular >

integral of 3^xln(3)

Solution

\int 3^{x} ln (3) d x

Solution

3^{x} + C

Solution steps

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

\int a^{x} d x = \frac{a ^{x}}{ln a}

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

Simplify

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

= 3^{x}

Add a constant to the solution

= 3^{x} + C

Popular Examples

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\int (q e^{q} + q) d q

integral of (5x)/(3x^2+1)

\int \frac{5 x}{3 x ^{2} + 1} d x

integral of (3x+108)/(x^2+2x-48)

\int \frac{3 x + 108}{x ^{2} + 2 x - 48} d x

integral of y^2 integral

y^{2}

integral of (sin^2(x/2))/(1-cos^2(x))

\int \frac{sin ^{2} ( \frac{x}{2} )}{1 - cos ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of 3^xln(3) ?
The integral of 3^xln(3) is 3^x+C