What is the integral of tan(t)sec^2(t) ?

The integral of tan(t)sec^2(t) is (tan^2(t))/2+C

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integral of tan(t)sec^2(t)

\int tan (t) sec^{2} (t) d t

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

Solution steps

\int tan (t) sec^{2} (t) d t

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 (t)

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

Add a constant to the solution

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

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What is the integral of tan(t)sec^2(t) ?
The integral of tan(t)sec^2(t) is (tan^2(t))/2+C