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

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

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

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

sec (x) + C

Solution steps

\int \frac{sin ( x )}{cos ^{2} ( x )} 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 y}{d x}, 9 x y = 5

\frac{s + 5}{( s + 2 ) ( s + 3 )}

x \to \infty lim (\frac{8}{x} - 8)

y = \frac{cos ( x )}{2 + sin ( x )}

cos (2 x + π)

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