What is the integral of 2^x(1+5^x) ?

The integral of 2^x(1+5^x) is (2^x)/(ln(2))+(10^x)/(ln(10))+C

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integral of 2^x(1+5^x)

\int 2^{x} (1 + 5^{x}) d x

\frac{2 ^{x}}{ln ( 2 )} + \frac{1 0 ^{x}}{ln ( 10 )} + C

Solution steps

\int 2^{x} (1 + 5^{x}) d x

Expand

2^{x} (1 + 5^{x}) : 2^{x} + 1 0^{x}

= \int 2^{x} + 1 0^{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 1 0^{x} d x

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

\int 1 0^{x} d x = \frac{1 0 ^{x}}{ln ( 10 )}

= \frac{2 ^{x}}{ln ( 2 )} + \frac{1 0 ^{x}}{ln ( 10 )}

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + \frac{1 0 ^{x}}{ln ( 10 )} + C

\frac{d y}{d t} = y^{\frac{1}{3}}, y (0) = 0

\int (ln (x))^{3} d x

f (x) = x^{2} + 3 x - 1, at x = 1

y^{^{''}} - 4 = 0

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

What is the integral of 2^x(1+5^x) ?
The integral of 2^x(1+5^x) is (2^x)/(ln(2))+(10^x)/(ln(10))+C