What is the integral of 1/(sec^2(x)) ?

The integral of 1/(sec^2(x)) is 1/2 (x+1/2 sin(2x))+C

Popular >

integral of 1/(sec^2(x))

integral

\frac{1}{sec ^{2} ( x )}

\frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1 + cos ( 2 x )}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int 1 + 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

= \frac{1}{2} (\int 1 d x + \int cos (2 x) d x)

\int 1 d x = x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

= \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Add a constant to the solution

= \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

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

\int \frac{ln ( x )}{x} (1 + ln (x)) d x

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

\int \frac{2 x ^{3}}{1 - x ^{2}} d x

\int (4 x - 6) x^{2} - 3 x d x

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