What is the integral of sec^2(x)-8cot(x) ?

The integral of sec^2(x)-8cot(x) is tan(x)-8ln|sin(x)|+C

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integral of sec^2(x)-8cot(x)

\int sec^{2} (x) - 8 cot (x) d x

tan (x) - 8 ln ∣ sin (x) ∣ + C

Solution steps

\int sec^{2} (x) - 8 cot (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sec^{2} (x) d x - \int 8 cot (x) d x

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

\int 8 cot (x) d x = 8 ln ∣ sin (x) ∣

= tan (x) - 8 ln ∣ sin (x) ∣

Add a constant to the solution

= tan (x) - 8 ln ∣ sin (x) ∣ + C

y^{^{''}} + 36 y = 24 sin (6 t)

y = \frac{1}{7 t ^{3}}

x \to 1 + lim ((1 - x)^{l n (x)})

\int_{2}^{3} \frac{38}{3 - x} d x

3 \frac{d y}{d x} = y^{2}

What is the integral of sec^2(x)-8cot(x) ?
The integral of sec^2(x)-8cot(x) is tan(x)-8ln|sin(x)|+C