What is the integral of (5^x-sec^2(x)) ?

The integral of (5^x-sec^2(x)) is (5^x)/(ln(5))-tan(x)+C

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integral of (5^x-sec^2(x))

\int (5^{x} - sec^{2} (x)) d x

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

Solution steps

\int 5^{x} - sec^{2} (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 5^{x} d x - \int sec^{2} (x) d x

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

\int sec^{2} (x) d x = tan (x)

= \frac{5 ^{x}}{ln ( 5 )} - tan (x)

Add a constant to the solution

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

\frac{\partial}{\partial y} (sin (3 x + yz))

\frac{\partial}{\partial x} (tan (3 x + 4 y))

\frac{x ^{2}}{x + 10}

e^{x} \frac{d x}{d t} = 3 t^{2}

\frac{( 3 x ^{2} - 6 ) ( x ^{2} - 2 )}{x ^{2} + 4}

What is the integral of (5^x-sec^2(x)) ?
The integral of (5^x-sec^2(x)) is (5^x)/(ln(5))-tan(x)+C