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

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

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

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

Solution steps

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

Rewrite using trig identities

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

\int (8 x - 3) d x

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

\int x^{6} + \frac{1}{x ^{6}} d x

\int sin^{5} (x) \cdot cos^{3} (x) d x

\int \frac{1}{2 t + 1} d t

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