What is the integral of ((csc(x)+cot(x))/(sin(x))) ?

The integral of ((csc(x)+cot(x))/(sin(x))) is -cot(x)-csc(x)+C

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integral of ((csc(x)+cot(x))/(sin(x)))

\int (\frac{csc ( x ) + cot ( x )}{sin ( x )}) d x

- cot (x) - csc (x) + C

Solution steps

\int \frac{csc ( x ) + cot ( x )}{sin ( x )} d x

Expand

\frac{csc ( x ) + cot ( x )}{sin ( x )} : \frac{csc ( x )}{sin ( x )} + \frac{cot ( x )}{sin ( x )}

= \int \frac{csc ( x )}{sin ( x )} + \frac{cot ( x )}{sin ( x )} d x

Apply the Sum Rule:

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

= \int \frac{csc ( x )}{sin ( x )} d x + \int \frac{cot ( x )}{sin ( x )} d x

\int \frac{csc ( x )}{sin ( x )} d x = - cot (x)

\int \frac{cot ( x )}{sin ( x )} d x = - csc (x)

= - cot (x) - csc (x)

Add a constant to the solution

= - cot (x) - csc (x) + C

\int x^{4035} e^{x^{2018}} d x

x \to 1 lim (x arcsin (\frac{x}{2}))

\frac{d}{d x} (3 \cdot 1 0^{2 x})

\int t ln (t + 1) d t

\frac{\partial}{\partial x} (2 (1 + y) x)

What is the integral of ((csc(x)+cot(x))/(sin(x))) ?
The integral of ((csc(x)+cot(x))/(sin(x))) is -cot(x)-csc(x)+C