What is the integral of (7cos(x))/(sqrt(sin(x))) ?

The integral of (7cos(x))/(sqrt(sin(x))) is 14sqrt(sin(x))+C

integral of (7cos(x))/(sqrt(sin(x)))

\int \frac{7 cos ( x )}{sin ( x )} d x

14 sin (x) + C

Solution steps

\int \frac{7 cos ( x )}{sin ( x )} d x

Take the constant out:

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

= 7 \cdot \int \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

= 7 \cdot \int \frac{1}{u} d u

Apply the Power Rule

= 7 \cdot 2 u^{\frac{1}{2}}

Substitute back

u = sin (x)

= 7 \cdot 2 sin^{\frac{1}{2}} (x)

Simplify

7 \cdot 2 sin^{\frac{1}{2}} (x) : 14 sin (x)

= 14 sin (x)

Add a constant to the solution

= 14 sin (x) + C

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What is the integral of (7cos(x))/(sqrt(sin(x))) ?
The integral of (7cos(x))/(sqrt(sin(x))) is 14sqrt(sin(x))+C