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

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

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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

Apply the Power Rule

= \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

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