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

The integral of (cos(x)+5^x) is sin(x)+(5^x)/(ln(5))+C

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integral of (cos(x)+5^x)

\int (cos (x) + 5^{x}) d x

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

Solution steps

\int cos (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 cos (x) d x + \int 5^{x} d x

\int cos (x) d x = sin (x)

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

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

Add a constant to the solution

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

\int (3^{x}) d x

y^{^{'}} = \frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8}

y = \frac{x ^{2} + 5}{x - 1}

\int (x^{2} + 6 x) cos (x) d x

\int \frac{8 + x + x ^{2}}{x} d x

What is the integral of (cos(x)+5^x) ?
The integral of (cos(x)+5^x) is sin(x)+(5^x)/(ln(5))+C