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Popular Calculus >

integral of 4^x

Solution

\int 4^{x} d x

Solution

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

Solution steps

\int 4^{x} d x

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

= \frac{4 ^{x}}{ln ( 4 )}

Simplify

\frac{4 ^{x}}{ln ( 4 )} : \frac{2 ^{2 x - 1}}{ln ( 2 )}

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

Add a constant to the solution

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

Graph

Popular Examples

derivative of f(x)=5x^2+4x-10

d er i v a t i v e f (x) = 5 x^{2} + 4 x - 10

integral of 3cos(x)+3sqrt(x)

\int 3 cos (x) + 3 x d x

(\partial)/(\partial x)(xe^{xy+1})

\frac{\partial}{\partial x} (x e^{x y + 1})

(\partial)/(\partial y)(2xsin(x^2y))

\frac{\partial}{\partial y} (2 x sin (x^{2} y))

derivative of 5x^2+3x-2

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

Frequently Asked Questions (FAQ)

What is the integral of 4^x ?
The integral of 4^x is (2^{2x-1})/(ln(2))+C