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

The integral of 3xsec^2(x) is 3(xtan(x)+ln|cos(x)|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 3xsec^2(x)

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

3 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

= 3 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 3 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 3 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 3 (x tan (x) + ln ∣ cos (x) ∣) + C

What is the integral of 3xsec^2(x) ?
The integral of 3xsec^2(x) is 3(xtan(x)+ln|cos(x)|)+C