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}

d er i v a t i v e ln (x e^{- 8 x})

\frac{d}{d x} (\frac{4 x}{4 + x})

\int (7 x + 6)^{4} d x

t \to 0 lim (\frac{6}{t} - \frac{6}{t ^{2} + t})

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