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Popular >

integral of 4^u

Solution

\int 4^{u} d u

Solution

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

Solution steps

\int 4^{u} d u

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

sum from n=1 to infinity of 2/(2^n)

n = 1 \sum \infty \frac{2}{2 ^{n}}

integral of x(sin^2(x))

\int x (sin^{2} (x)) d x

2y^{''}+16y^'+32y=0,y(0)=-3,y^'(0)=10

2 y^{^{''}} + 16 y^{^{'}} + 32 y = 0, y (0) = - 3, y^{^{'}} (0) = 10

derivative of {f}(x(x)^3(x))

\frac{d}{d x} (f (x) (x)^{3} (x))

tangent of f(x)=cos(2x)tangent of

f (x) = cos (2 x)

Frequently Asked Questions (FAQ)

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