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

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

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integral of sec^2(θ)tan(θ)

\int sec^{2} (θ) tan (θ) d θ

\frac{tan ^{2} ( θ )}{2} + C

Solution steps

\int sec^{2} (θ) tan (θ) d θ

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 (θ)

= \frac{tan ^{2} ( θ )}{2}

Add a constant to the solution

= \frac{tan ^{2} ( θ )}{2} + C

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