What is the integral of sec(x)(7sec(x)+6tan(x)) ?

The integral of sec(x)(7sec(x)+6tan(x)) is 7tan(x)+6sec(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)(7sec(x)+6tan(x))

\int sec (x) (7 sec (x) + 6 tan (x)) d x

7 tan (x) + 6 sec (x) + C

Solution steps

\int sec (x) (7 sec (x) + 6 tan (x)) d x

Rewrite using trig identities

= \int \frac{7 + 6 sin ( x )}{cos ^{2} ( x )} d x

Expand

\frac{7 + 6 sin ( x )}{cos ^{2} ( x )} : \frac{7}{cos ^{2} ( x )} + \frac{6 sin ( x )}{cos ^{2} ( x )}

= \int \frac{7}{cos ^{2} ( x )} + \frac{6 sin ( x )}{cos ^{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{7}{cos ^{2} ( x )} d x + \int \frac{6 sin ( x )}{cos ^{2} ( x )} d x

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

\int \frac{6 sin ( x )}{cos ^{2} ( x )} d x = 6 sec (x)

= 7 tan (x) + 6 sec (x)

Add a constant to the solution

= 7 tan (x) + 6 sec (x) + C

\int 7 x cos (x^{2} - 3) d x

\int \frac{1 + 4 cot ( x )}{4 - cot ( x )} d x

\int cot^{3} (d) x d x

\int (cot^{2} (x) + 1)^{2} csc^{2} (x) d x

\int x (2 x + 3)^{7} d x

What is the integral of sec(x)(7sec(x)+6tan(x)) ?
The integral of sec(x)(7sec(x)+6tan(x)) is 7tan(x)+6sec(x)+C