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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3/x+sec^2(x))

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

3 ln ∣ x ∣ + tan (x) + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ + tan (x)

Add a constant to the solution

= 3 ln ∣ x ∣ + tan (x) + C

\int (3 x + 1)^{\frac{3}{2}} d x

\int \frac{4 x + 5}{x ^{2} + x - 2} d x

\int y^{6} (y^{2} + 4 y - 5) d y

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

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

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