What is the integral of 4/x+csc(x)cot(x) ?

The integral of 4/x+csc(x)cot(x) is 4ln|x|-csc(x)+C

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integral of 4/x+csc(x)cot(x)

\int \frac{4}{x} + csc (x) cot (x) d x

4 ln ∣ x ∣ - csc (x) + C

Solution steps

\int \frac{4}{x} + csc (x) cot (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{4}{x} d x + \int csc (x) cot (x) d x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int csc (x) cot (x) d x = - csc (x)

= 4 ln ∣ x ∣ - csc (x)

Add a constant to the solution

= 4 ln ∣ x ∣ - csc (x) + C

\frac{d}{d x} (\frac{4 x}{1 + x ^{2}})

\frac{d y}{d x} = \frac{y}{x ^{2}}, y (1) = 1

x \to 1 + lim (\frac{4}{x ^{(1 - x)}})

\frac{d}{d x} (sec^{2} (x) - 1)

\int_{0}^{\frac{π}{2}} \frac{1}{x ^{2} + 2} d x

What is the integral of 4/x+csc(x)cot(x) ?
The integral of 4/x+csc(x)cot(x) is 4ln|x|-csc(x)+C