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

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

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integral of 2sec^2(θ)tan(θ)

\int 2 sec^{2} (θ) tan (θ) d θ

tan^{2} (θ) + C

Solution steps

\int 2 sec^{2} (θ) tan (θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int u d u

= 2 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

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

Substitute back

u = tan (θ)

= 2 \cdot \frac{tan ^{2} ( θ )}{2}

Simplify

2 \cdot \frac{tan ^{2} ( θ )}{2} : tan^{2} (θ)

= tan^{2} (θ)

Add a constant to the solution

= tan^{2} (θ) + C

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