What is the integral of-sin(x)+1/(cos^2(x)) ?

The integral of-sin(x)+1/(cos^2(x)) is cos(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-sin(x)+1/(cos^2(x))

\int - sin (x) + \frac{1}{cos ^{2} ( x )} d x

cos (x) + tan (x) + C

Solution steps

\int - sin (x) + \frac{1}{cos ^{2} ( x )} d x

Use the basic trigonometric identity:

\frac{1}{cos ( x )} = sec (x)

= \int - sin (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 sin (x) d x + \int sec^{2} (x) d x

\int sin (x) d x = - cos (x)

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

= - (- cos (x)) + tan (x)

Simplify

= cos (x) + tan (x)

Add a constant to the solution

= cos (x) + tan (x) + C

\int x^{2} - ln (x^{2}) + k d x

\int_{1}^{5} 1 d x

\int x^{2} \cdot e^{- a x} d x

\frac{1}{( x - 1 )}

x \to 2 lim (ln (\frac{x}{x ^{2} - 4}))

What is the integral of-sin(x)+1/(cos^2(x)) ?
The integral of-sin(x)+1/(cos^2(x)) is cos(x)+tan(x)+C