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

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

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integral of-tan^2(x)

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

x - tan (x) + C

Solution steps

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

Take the constant out:

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

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

Rewrite using trig identities

= - \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

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

\int 1 d x = x

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

= - (- x + tan (x))

Simplify

= x - tan (x)

Add a constant to the solution

= x - tan (x) + C

\int \frac{x}{121 x ^{2} - 1} d x

y = 2^{- x}

\int (2 w^{2} - w) e^{7 w - 1} d w

\int \frac{4 - x ^{2}}{2 + x} d x

\frac{d y}{d t} = 3 y