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

The integral of ((sin(x))/(cos(x)))^2 is -x+tan(x)+C

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

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

- x + tan (x) + C

Solution steps

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

Rewrite using trig identities

= \int - 1 + sec^{2} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1 d x + \int sec^{2} (x) d x

\int 1 d x = x

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

= - x + tan (x)

Add a constant to the solution

= - x + tan (x) + C

\int \frac{1}{1 + x - 1} d x

\int \frac{1}{( x ^{\frac{2}{3}} ) ( 1 + x ^{\frac{2}{3}} )} d x

\int \frac{4 x ^{2}}{1 + x ^{3}} d x

\int 6 x - 3 x^{2} d x

\int \frac{3 x ^{2}}{x ^{3} + 4} d x

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