What is the integral of (3^x-sec^2(x)) ?

The integral of (3^x-sec^2(x)) is (3^x)/(ln(3))-tan(x)+C

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integral of (3^x-sec^2(x))

\int (3^{x} - sec^{2} (x)) d x

\frac{3 ^{x}}{ln ( 3 )} - tan (x) + C

Solution steps

\int 3^{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 3^{x} d x - \int sec^{2} (x) d x

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

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

= \frac{3 ^{x}}{ln ( 3 )} - tan (x)

Add a constant to the solution

= \frac{3 ^{x}}{ln ( 3 )} - tan (x) + C

\frac{d y}{d x} = - 4 x + 6 x^{2}

x \to 4 lim (x^{2} + 1)

e^{x}

f (x) = \frac{x ^{3}}{6} + \frac{1}{2 x}

\frac{d}{d x} (\frac{1 + cos ( x )}{sin ( x )})

What is the integral of (3^x-sec^2(x)) ?
The integral of (3^x-sec^2(x)) is (3^x)/(ln(3))-tan(x)+C