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

The integral of (tan(y))/(cos^2(y)) is (tan^2(y))/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(y))/(cos^2(y))

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

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

Solution steps

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

Rewrite using trig identities

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

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 (y)

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

Add a constant to the solution

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

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

\int \frac{2 x + 9}{x ^{2} + 9 x + 2} d x

\int (7 - 4 x)^{11} d x

\int \frac{1}{7 + e ^{x}} d x

\int \frac{4 x}{1 - 4 x ^{4}} d x

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