What is the integral of (cos^3(x))/(1-sin(x)) ?

The integral of (cos^3(x))/(1-sin(x)) is (sin^2(x))/2+sin(x)+C

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integral of (cos^3(x))/(1-sin(x))

\int \frac{cos ^{3} ( x )}{1 - sin ( x )} d x

\frac{sin ^{2} ( x )}{2} + sin (x) + C

Solution steps

\int \frac{cos ^{3} ( x )}{1 - sin ( x )} d x

Apply Trigonometric Substitution

: \int u + 1 d u

= \int u + 1 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u + \int 1 d u

\int u d u = \frac{u ^{2}}{2}

\int 1 d u = u

= \frac{u ^{2}}{2} + u

Substitute back

u = sin (x)

= \frac{sin ^{2} ( x )}{2} + sin (x)

Add a constant to the solution

= \frac{sin ^{2} ( x )}{2} + sin (x) + C

\frac{d}{d x} (se xx)

\int_{- 1}^{- 0.5} 1.5 x^{2} d x

(1 - x^{2}) y^{^{''}} - x y^{^{'}} + y = 0

x \to 0 lim (\frac{x ^{2} - 4}{x})

x^{4} - 4 x^{2}, x^{2} - 4

What is the integral of (cos^3(x))/(1-sin(x)) ?
The integral of (cos^3(x))/(1-sin(x)) is (sin^2(x))/2+sin(x)+C