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

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

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

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

sec (x) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= \int - \frac{1}{u ^{2}} d u

Take the constant out:

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

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = cos (x)

= - (- \frac{1}{cos ( x )})

Simplify

- (- \frac{1}{cos ( x )}) : sec (x)

= sec (x)

Add a constant to the solution

= sec (x) + C

\frac{d}{d x} (arcsin (6 x) + arccos (6 x))

\frac{\partial}{\partial t} (t^{2} - 2)

f (x) = x 6 - x

\frac{\partial}{\partial x} (30 x^{\frac{3}{4}} y^{\frac{1}{4}})

\frac{d}{d x} (\frac{9 + 2 x - 4 x}{x})

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