What is the integral of (sin(x))/(sqrt(cos^3(x))) ?

The integral of (sin(x))/(sqrt(cos^3(x))) is 2/(sqrt(cos(x)))+C

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integral of (sin(x))/(sqrt(cos^3(x)))

\int \frac{sin ( x )}{cos ^{3} ( x )} d x

\frac{2}{cos ( x )} + C

Solution steps

\int \frac{sin ( x )}{cos ^{3} ( x )} d x

Apply u-substitution

: \int - \frac{1}{u ^{\frac{3}{2}}} d u

= \int - \frac{1}{u ^{\frac{3}{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 ^{\frac{3}{2}}} d u

Apply the Power Rule

: - \frac{2}{u}

= - (- \frac{2}{u})

Substitute back

u = cos (x)

= - (- \frac{2}{cos ( x )})

Simplify

= \frac{2}{cos ( x )}

Add a constant to the solution

= \frac{2}{cos ( x )} + C

\frac{d}{d x} (x - \frac{1}{2} x^{2})

\frac{d y}{d x} = sin (7 e^{x})

\int sec^{2} (θ) tan^{9} (θ) d θ

x \to 4 lim (4)

y^{^{''}} = 4 sin (7 x)

What is the integral of (sin(x))/(sqrt(cos^3(x))) ?
The integral of (sin(x))/(sqrt(cos^3(x))) is 2/(sqrt(cos(x)))+C