What is the integral of tan(x)+4^x ?

The integral of tan(x)+4^x is -ln|cos(x)|+(2^{2x-1})/(ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of tan(x)+4^x

\int tan (x) + 4^{x} d x

- ln ∣ cos (x) ∣ + \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

Solution steps

\int tan (x) + 4^{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 tan (x) d x + \int 4^{x} d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int 4^{x} d x = \frac{2 ^{2 x - 1}}{ln ( 2 )}

= - ln ∣ cos (x) ∣ + \frac{2 ^{2 x - 1}}{ln ( 2 )}

Add a constant to the solution

= - ln ∣ cos (x) ∣ + \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

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

y = x^{2} - 7, y = 2

x \to 2 lim (- x^{3} + 2 x^{2} - 1)

\frac{d}{d x} (arctan (1 + x^{2}))

(\frac{100}{ln ( 2 x + 1 )})^{^{'}}

What is the integral of tan(x)+4^x ?
The integral of tan(x)+4^x is -ln|cos(x)|+(2^{2x-1})/(ln(2))+C