What is the integral of sec(x)(2sec(x)+7tan(x)) ?

The integral of sec(x)(2sec(x)+7tan(x)) is 2tan(x)+7sec(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sec(x)(2sec(x)+7tan(x))

\int sec (x) (2 sec (x) + 7 tan (x)) d x

2 tan (x) + 7 sec (x) + C

Solution steps

\int sec (x) (2 sec (x) + 7 tan (x)) d x

Rewrite using trig identities

= \int \frac{2 + 7 tan ( x ) cos ( x )}{cos ^{2} ( x )} d x

Expand

\frac{2 + 7 tan ( x ) cos ( x )}{cos ^{2} ( x )} : \frac{2}{cos ^{2} ( x )} + \frac{7 tan ( x )}{cos ( x )}

= \int \frac{2}{cos ^{2} ( x )} + \frac{7 tan ( x )}{cos ( 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{2}{cos ^{2} ( x )} d x + \int \frac{7 tan ( x )}{cos ( x )} d x

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

\int \frac{7 tan ( x )}{cos ( x )} d x = 7 sec (x)

= 2 tan (x) + 7 sec (x)

Add a constant to the solution

= 2 tan (x) + 7 sec (x) + C

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

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

\int sec^{2} (x) (e^{t a n (x)}) d x

\int \frac{x + 3}{x ^{2} - 2 x - 5} d x

\int 1 - e^{- 2 x} d x

What is the integral of sec(x)(2sec(x)+7tan(x)) ?
The integral of sec(x)(2sec(x)+7tan(x)) is 2tan(x)+7sec(x)+C