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

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

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integral of sec(t)(sec(t)tan(t))

\int sec (t) (sec (t) tan (t)) d t

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

Solution steps

\int sec (t) sec (t) tan (t) d t

Apply u-substitution

= \int u d u

Apply the Power Rule

= \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

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