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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = tan (z)

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

Add a constant to the solution

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

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