What is the integral of (tan(x))/(cos^2(x)) ?

The integral of (tan(x))/(cos^2(x)) is (tan^2(x))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (tan(x))/(cos^2(x))

integral

\frac{tan ( x )}{cos ^{2} ( x )}

\frac{tan ^{2} ( x )}{2} + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = tan (x)

= \frac{tan ^{2} ( x )}{2}

Add a constant to the solution

= \frac{tan ^{2} ( x )}{2} + C

cot (\frac{x}{2})

\frac{x ^{2}}{( 2 + x )}

\frac{1}{( a - 2 x ) ^{2}}

\frac{cos ^{3} ( x )}{sin ( x )}

\frac{x}{2 + 3}

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