What is the integral of-4tan(x) ?

The integral of-4tan(x) is 4ln|cos(x)|+C

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integral of-4tan(x)

\int - 4 tan (x) d x

4 ln ∣ cos (x) ∣ + C

Solution steps

\int - 4 tan (x) d x

Take the constant out:

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

= - 4 \cdot \int tan (x) d x

Rewrite using trig identities

= - 4 \cdot \int \frac{sin ( x )}{cos ( x )} d x

Apply u-substitution

: \int - \frac{1}{u} d u

= - 4 \cdot \int - \frac{1}{u} d u

Take the constant out:

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

= - 4 (- \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 4 (- ln ∣ u ∣)

Substitute back

u = cos (x)

= - 4 (- ln ∣ cos (x) ∣)

Simplify

= 4 ln ∣ cos (x) ∣

Add a constant to the solution

= 4 ln ∣ cos (x) ∣ + C

\int 35 sec^{- 2} (x t a) n^{3} x d x

x \to 1 lim (\frac{1 - x}{x ^{2} - 1})

(- \frac{1}{x})^{^{'}}

y^{^{''}} + 2 y^{^{'}} = 2 x + 9 - e^{- 2 x}

\frac{6 s + 4}{s ^{2} + 4 s + 20}