What is the integral of-sec^3(x) ?

The integral of-sec^3(x) is -1/2 sec(x)tan(x)-1/2 ln|tan(x)+sec(x)|+C

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integral of-sec^3(x)

\int - sec^{3} (x) d x

- \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int - sec^{3} (x) d x

Take the constant out:

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

= - \int sec^{3} (x) d x

Apply Integral Reduction

= - (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} \cdot \int sec (x) d x)

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= - (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Simplify

- (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) : - \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

= - \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= - \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

f (x)^{2}

\frac{d}{d x} ((2 x + 1)^{\frac{1}{2}})

\frac{d}{d x} (\frac{2}{( x + 2 ) ^{2}})

n = 1 \sum \infty 0. 9^{n} n^{3}

\int_{10}^{13} 2 x d x

What is the integral of-sec^3(x) ?
The integral of-sec^3(x) is -1/2 sec(x)tan(x)-1/2 ln|tan(x)+sec(x)|+C