What is the integral of sin(x) 1/(cos(x)) ?

The integral of sin(x) 1/(cos(x)) is -ln|cos(x)|+C

Popular >

integral of sin(x) 1/(cos(x))

\int sin (x) \frac{1}{cos ( x )} d x

- ln ∣ cos (x) ∣ + C

Solution steps

\int sin (x) \frac{1}{cos ( x )} d x

Simplify

sin (x) \frac{1}{cos ( x )} : tan (x)

= \int tan (x) d x

Rewrite using trig identities

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cos (x)

= - ln ∣ cos (x) ∣

Add a constant to the solution

= - ln ∣ cos (x) ∣ + C

\frac{3 x ^{2} - 1}{2 x x}

\int (2 x)^{3} 2 d x

x \to 2 lim (\frac{1}{4 - x ^{2}})

\int \frac{x ^{4}}{( 2 - x ^{5} ) ^{4}} d x

y = \frac{4 x ^{2} + 6 x + 2}{x}

What is the integral of sin(x) 1/(cos(x)) ?
The integral of sin(x) 1/(cos(x)) is -ln|cos(x)|+C