Integral of sec²x

Q: What is the integral of sec²x?

\int \sec^{2}\left(x\right)\,dx = \tan\left(x\right) + C.

Q: How can I check the answer?

Differentiate it: the derivative of \tan\left(x\right) is \sec^{2}\left(x\right). CalcViz checks every antiderivative this way before showing it.

\int \sec^{2}\left(x\right)\,dx = \tan\left(x\right) + C

A direct reversal of d/dx tan x = sec²x.

Step by step

Trig rule
∫sec²u du = tan u.
$\int \sec^{2}\left(x\right)\,dx = \tan\left(x\right)$

f(x) = sec²x
F(x) + C

Constant C = 0.0

Every choice of C gives a valid antiderivative, since shifting up or down doesn’t change the slope.

Open in the integral calculator

Questions students ask

What is the integral of sec²x?

$\int \sec^{2}\left(x\right)\,dx = \tan\left(x\right) + C$ .

How do you integrate sec²x?

A direct reversal of d/dx tan x = sec²x.

How can I check the answer?

Differentiate it: the derivative of $\tan\left(x\right)$ is $\sec^{2}\left(x\right)$ . CalcViz checks every antiderivative this way before showing it.