What is the integral of (tan(x))/((sin(x))^2) ?

The integral of (tan(x))/((sin(x))^2) is ln|tan(x)|+C

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integral of (tan(x))/((sin(x))^2)

\int \frac{tan ( x )}{( sin ( x ) ) ^{2}} d x

ln ∣ tan (x) ∣ + C

Solution steps

\int \frac{tan ( x )}{( sin ( x ) ) ^{2}} d x

Rewrite using trig identities

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

Apply Trigonometric Substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = tan (x)

= ln ∣ tan (x) ∣

Add a constant to the solution

= ln ∣ tan (x) ∣ + C

\int 6 x^{- \frac{4}{5}} d x

\int 3 x^{4} + 3 (x^{3}) d x

\int (x^{2} + 3 x - 5) ln (x) d x

\int cos (l) n x \frac{1}{x} d x

1 + (\frac{1}{4 x})

What is the integral of (tan(x))/((sin(x))^2) ?
The integral of (tan(x))/((sin(x))^2) is ln|tan(x)|+C