What is the integral of-6tan^2(x) ?

The integral of-6tan^2(x) is -6(-x+tan(x))+C

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integral of-6tan^2(x)

\int - 6 tan^{2} (x) d x

- 6 (- x + tan (x)) + C

Solution steps

\int - 6 tan^{2} (x) d x

Take the constant out:

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

= - 6 \cdot \int tan^{2} (x) d x

Rewrite using trig identities

= - 6 \cdot \int - 1 + sec^{2} (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

= - 6 (- \int 1 d x + \int sec^{2} (x) d x)

\int 1 d x = x

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

= - 6 (- x + tan (x))

Add a constant to the solution

= - 6 (- x + tan (x)) + C

x^{3} \frac{d y}{d x} + (2 - 3 x^{2}) y = x^{3}

x \to 1 lim (\frac{x ^{3}}{x - 1})

\frac{2}{s - 3}

f (x) = x^{2} + 2, (5, 27)

10 sin (x) cos (x)

What is the integral of-6tan^2(x) ?
The integral of-6tan^2(x) is -6(-x+tan(x))+C