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

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

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

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

tan^{2} (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \int u d u

Apply the Power Rule

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

Substitute back

u = tan (x)

= 2 \cdot \frac{tan ^{2} ( x )}{2}

Simplify

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

= tan^{2} (x)

Add a constant to the solution

= tan^{2} (x) + C

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