What is the integral of 6sec^3(x) ?

The integral of 6sec^3(x) is 6(1/2 sec(x)tan(x)+1/2 ln|tan(x)+sec(x)|)+C

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integral of 6sec^3(x)

\int 6 sec^{3} (x) d x

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

Solution steps

\int 6 sec^{3} (x) d x

Take the constant out:

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

= 6 \cdot \int sec^{3} (x) d x

Apply Integral Reduction

= 6 (\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) ∣

= 6 (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Simplify

6 (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) : 6 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

= 6 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= 6 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) + C

\frac{d}{d x} (\frac{2}{x - 11})

x \to 9 lim (\frac{6}{( x - 9 ) ^{2}})

x \to 0 lim (\frac{x}{x + x ^{2}})

x \to 0 lim (3 x - 2)

\int x x + 5 d x

What is the integral of 6sec^3(x) ?
The integral of 6sec^3(x) is 6(1/2 sec(x)tan(x)+1/2 ln|tan(x)+sec(x)|)+C