What is the integral of cos(x)csc^9(x) ?

The integral of cos(x)csc^9(x) is -1/8 csc^8(x)+C

Popular >

integral of cos(x)csc^9(x)

\int cos (x) csc^{9} (x) d x

- \frac{1}{8} csc^{8} (x) + C

Solution steps

\int cos (x) csc^{9} (x) d x

Rewrite using trig identities

= \int \frac{cos ( x )}{sin ^{9} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{9}} d u

= \int \frac{1}{u ^{9}} d u

Apply the Power Rule

: - \frac{1}{8 u ^{8}}

= - \frac{1}{8 u ^{8}}

Substitute back

u = sin (x)

= - \frac{1}{8 sin ^{8} ( x )}

Simplify

- \frac{1}{8 sin ^{8} ( x )} : - \frac{1}{8} csc^{8} (x)

= - \frac{1}{8} csc^{8} (x)

Add a constant to the solution

= - \frac{1}{8} csc^{8} (x) + C

x^{3} y^{^{'''}} + 6 y = 0

\int 4 sin (θ) d θ

x \to 1 lim (3 x^{3} - 4 x^{2} + x + 9)

x \to 1 - lim (x^{3} + 1)

f (x) = x^{2} + 5 x + 6

What is the integral of cos(x)csc^9(x) ?
The integral of cos(x)csc^9(x) is -1/8 csc^8(x)+C