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Popular >

integral of 3^xe^x

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

3^{x} e^{x} = (3 e)^{x}

= \int (3 e)^{x} d x

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

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

Add a constant to the solution

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

Popular Examples

derivative of sin(x+csc(x))

\frac{d}{d x} (sin (x) + csc (x))

(xdy)/(dx)=2xe^x-y+6x^2

\frac{x d y}{d x} = 2 x e^{x} - y + 6 x^{2}

y^{''}+2y^'+y=x^2

y^{^{''}} + 2 y^{^{'}} + y = x^{2}

derivative of 1/3 x^3-1/2 x^2-30x+2 derivative of

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 30 x + 2

tangent of y=(2x+3)/(3x-2)tangent of

y = \frac{2 x + 3}{3 x - 2}

Frequently Asked Questions (FAQ)

What is the integral of 3^xe^x ?
The integral of 3^xe^x is ((3e)^x)/(ln(3e))+C