What is the integral of (-7-7tan^2(x)) ?

The integral of (-7-7tan^2(x)) is -7tan(x)+C

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integral of (-7-7tan^2(x))

\int (- 7 - 7 tan^{2} (x)) d x

- 7 tan (x) + C

Solution steps

\int - 7 - 7 tan^{2} (x) d x

Factor out common term

- 7

= \int - 7 (tan^{2} (x) + 1) d x

Take the constant out:

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

= - 7 \cdot \int tan^{2} (x) + 1 d x

Rewrite using trig identities

= - 7 \cdot \int sec^{2} (x) d x

Use the common integral:

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

= - 7 tan (x)

Add a constant to the solution

= - 7 tan (x) + C

x \frac{d y}{d x} - 3 y = y^{2}, y (1) = 3

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

\int 5 cos (x) + 2 sin (x) d x

f (x) = 3 x^{\frac{2}{3}} - 3, at x = 27

\frac{d}{d x} (12 x^{\frac{1}{2}})

What is the integral of (-7-7tan^2(x)) ?
The integral of (-7-7tan^2(x)) is -7tan(x)+C