What is the integral of (cos(pi*x))/(sin(pi*x)) ?

The integral of (cos(pi*x))/(sin(pi*x)) is xcot(pix)-(-pi 1/(pi^2)(-pixcot(pix)-(-ln|sin(pix)|)))+C

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integral of (cos(pix))/(sin(pix))

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

x cot (π x) - (- π \frac{1}{π ^{2}} (- π x cot (π x) - (- ln ∣ sin (π x) ∣))) + C

Solution steps

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

Rewrite using trig identities

= \int cot (π x) d x

Apply Integration By Parts

: x cot (π x) - \int - π x csc^{2} (π x) d x

= x cot (π x) - \int - π x csc^{2} (π x) d x

\int - π x csc^{2} (π x) d x = - π \frac{1}{π ^{2}} (- π x cot (π x) - (- ln ∣ sin (π x) ∣))

= x cot (π x) - (- π \frac{1}{π ^{2}} (- π x cot (π x) - (- ln ∣ sin (π x) ∣)))

Add a constant to the solution

= x cot (π x) - (- π \frac{1}{π ^{2}} (- π x cot (π x) - (- ln ∣ sin (π x) ∣))) + C

\frac{d y}{d x} = e^{2 x + y}

\frac{d y}{d x} = x e^{x^{2} - l n (y^{2})}

\int_{- 2}^{3} (10 x^{3} - 4 x) (x + 2) d x

f (x) = x sin (\frac{2}{x})

x \to 2 + lim (2 - x^{2})

What is the integral of (cos(pi*x))/(sin(pi*x)) ?
The integral of (cos(pi*x))/(sin(pi*x)) is xcot(pix)-(-pi 1/(pi^2)(-pixcot(pix)-(-ln|sin(pix)|)))+C