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Popular >

integral of e^xa^x

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

x^2y^'+y= x/y ,y(1)=4

x^{2} y^{^{'}} + y = \frac{x}{y}, y (1) = 4

area f(x)=x+2,-2,1 area

f (x) = x + 2, - 2, 1

((y^'-e-t+4))/y =-4

\frac{( y ^{^{'}} - e - t + 4 )}{y} = - 4

limit as x approaches 0 of (7^{sin(x)}-1)/x

x \to 0 lim (\frac{7 ^{s i n (x)} - 1}{x})

integral of x^2*cos^3(7)x^3

\int x^{2} \cdot cos^{3} (7) x^{3} d x

Frequently Asked Questions (FAQ)

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