What is the integral of (4^x+10^x)/(2^x) ?

The integral of (4^x+10^x)/(2^x) is (2^x)/(ln(2))+(5^x)/(ln(5))+C

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integral of (4^x+10^x)/(2^x)

\int \frac{4 ^{x} + 1 0 ^{x}}{2 ^{x}} d x

\frac{2 ^{x}}{ln ( 2 )} + \frac{5 ^{x}}{ln ( 5 )} + C

Solution steps

\int \frac{4 ^{x} + 1 0 ^{x}}{2 ^{x}} d x

Expand

\frac{4 ^{x} + 1 0 ^{x}}{2 ^{x}} : 2^{x} + 5^{x}

= \int 2^{x} + 5^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2^{x} d x + \int 5^{x} d x

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

\int 5^{x} d x = \frac{5 ^{x}}{ln ( 5 )}

= \frac{2 ^{x}}{ln ( 2 )} + \frac{5 ^{x}}{ln ( 5 )}

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + \frac{5 ^{x}}{ln ( 5 )} + C

\int \frac{1}{x ( 1 + x )} d x

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

\frac{d}{d x} (cos^{3} (x^{2} - 1))

x \to + 0 + lim (x^{\frac{2}{x}})

y^{^{''}} + 15 y^{^{'}} + 54 y = 0

What is the integral of (4^x+10^x)/(2^x) ?
The integral of (4^x+10^x)/(2^x) is (2^x)/(ln(2))+(5^x)/(ln(5))+C