What is the integral of sin(x)sec(x) ?

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

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integral of sin(x)sec(x)

\int sin (x) sec (x) d x

- ln ∣ cos (x) ∣ + C

Solution steps

\int sin (x) sec (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{d}{d x} (sin (x) \cdot tan (x))

\frac{d x}{d t} = a x - b x^{2} - 0

\frac{2 x ^{2} + 4 x + 2}{x}

y = 4 x^{3} - 4 x

\int_{- 1}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

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