Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

What is the antiderivative of ${sec}^{2} (x)$ $sec^2(x)$ ?

1 Answer

Jan 25, 2016

$tan x + C$ $tanx +C$

Explanation:

$\frac{d}{d x} (tan x) = {sec}^{2} x$ $d/dx(tanx) =sec^2x$ ,

so $tan x$ $tanx$ in an antiderivative of ${sec}^{2} x$ $sec^2x$

and the general antiderivative of ${sec}^{2} x$ $sec^2x$ is $tan x + C$ $tanx+C$ .

Related questions

How do I evaluate the indefinite integral $\int {sin}^{3} (x) \cdot {cos}^{2} (x) d x$ $intsin^3(x)*cos^2(x)dx$ ?
How do I evaluate the indefinite integral $\int {sin}^{6} (x) \cdot {cos}^{3} (x) d x$ $intsin^6(x)*cos^3(x)dx$ ?
How do I evaluate the indefinite integral $\int {cos}^{5} (x) d x$ $intcos^5(x)dx$ ?
How do I evaluate the indefinite integral $\int {sin}^{2} (2 t) d t$ $intsin^2(2t)dt$ ?
How do I evaluate the indefinite integral $\int {(1 + cos (x))}^{2} d x$ $int(1+cos(x))^2dx$ ?
How do I evaluate the indefinite integral $\int {sec}^{2} (x) \cdot tan (x) d x$ $intsec^2(x)*tan(x)dx$ ?
How do I evaluate the indefinite integral $\int {cot}^{5} (x) \cdot {sin}^{4} (x) d x$ $intcot^5(x)*sin^4(x)dx$ ?
How do I evaluate the indefinite integral $\int {tan}^{2} (x) d x$ $inttan^2(x)dx$ ?
How do I evaluate the indefinite integral $\int {({tan}^{2} (x) + {tan}^{4} (x))}^{2} d x$ $int(tan^2(x)+tan^4(x))^2dx$ ?
How do I evaluate the indefinite integral $\int x \cdot sin (x) \cdot tan (x) d x$ $intx*sin(x)*tan(x)dx$ ?

See all questions in Integrals of Trigonometric Functions

Impact of this question

122066 views around the world

You can reuse this answer
Creative Commons License