What is the integral of-(3sin(-x))/(cos(-x)) ?

The integral of-(3sin(-x))/(cos(-x)) is -3ln|cos(x)|+C

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integral of-(3sin(-x))/(cos(-x))

\int - \frac{3 sin ( - x )}{cos ( - x )} d x

- 3 ln ∣ cos (x) ∣ + C

Solution steps

\int - \frac{3 sin ( - x )}{cos ( - x )} d x

Take the constant out:

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

= - 3 \cdot \int \frac{sin ( - x )}{cos ( - x )} d x

Rewrite using trig identities

= - 3 \cdot \int tan (- x) d x

Apply Integration By Parts

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

= - 3 (- \int - x sec^{2} (x) d x - x tan (x))

\int - x sec^{2} (x) d x = - x tan (x) - ln ∣ cos (x) ∣

= - 3 (- (- x tan (x) - ln ∣ cos (x) ∣) - x tan (x))

Simplify

= - 3 ln ∣ cos (x) ∣

Add a constant to the solution

= - 3 ln ∣ cos (x) ∣ + C

\int_{- 1}^{1} π (8 - 8 x^{2})^{2} d x

f (x) = x - (x + 1)^{4}

y^{^{'}} = x - 7

e^{x} (4 - x)

\int \frac{9 r ^{2}}{1 - r ^{3}} d r

What is the integral of-(3sin(-x))/(cos(-x)) ?
The integral of-(3sin(-x))/(cos(-x)) is -3ln|cos(x)|+C