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

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

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

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

- \frac{tan ^{2} ( x )}{2} + C

Solution steps

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

Take the constant out:

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

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

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 (x)

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

Add a constant to the solution

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

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