What is the integral of cos(x)csc^{10}(x) ?

The integral of cos(x)csc^{10}(x) is -1/9 csc^9(x)+C

integral of cos(x)csc^{10}(x)

\int cos (x) csc^{10} (x) d x

- \frac{1}{9} csc^{9} (x) + C

Solution steps

\int cos (x) csc^{10} (x) d x

Rewrite using trig identities

= \int \frac{cos ( x )}{sin ^{10} ( x )} d x

Apply u-substitution

= \int \frac{1}{u ^{10}} d u

Apply the Power Rule

= - \frac{1}{9 u ^{9}}

Substitute back

u = sin (x)

= - \frac{1}{9 sin ^{9} ( x )}

Simplify

- \frac{1}{9 sin ^{9} ( x )} : - \frac{1}{9} csc^{9} (x)

= - \frac{1}{9} csc^{9} (x)

Add a constant to the solution

= - \frac{1}{9} csc^{9} (x) + C

\frac{\partial}{\partial x} (\frac{x + 4}{x + 5})

\frac{\partial}{\partial y} (sin (\frac{y}{x}))

\frac{d}{d x} (\frac{1}{x ( x + 2 )})

t an g e n t (3 x^{2} + 2 x), at (a = - 3)

a re a y = x, y = x - 2, [0, 4]

What is the integral of cos(x)csc^{10}(x) ?
The integral of cos(x)csc^{10}(x) is -1/9 csc^9(x)+C