What is the integral of (1/x+cot(x)-sec(x)) ?

The integral of (1/x+cot(x)-sec(x)) is ln|x|+ln|sin(x)|-ln|tan(x)+sec(x)|+C

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integral of (1/x+cot(x)-sec(x))

\int (\frac{1}{x} + cot (x) - sec (x)) d x

ln ∣ x ∣ + ln ∣ sin (x) ∣ - ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{1}{x} + cot (x) - sec (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{1}{x} d x + \int cot (x) d x - \int sec (x) d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int cot (x) d x = ln ∣ sin (x) ∣

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= ln ∣ x ∣ + ln ∣ sin (x) ∣ - ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ x ∣ + ln ∣ sin (x) ∣ - ln ∣ tan (x) + sec (x) ∣ + C

e^{3 \cdot x} \cdot (2 \cdot sin (4 \cdot x))

\int \frac{1}{( 2 y + 5 ) ^{2}} d y

n = 1 \sum \infty (\frac{2}{3})^{n}

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{2 y}

\int_{- 1}^{2} 1 + x^{2} d x

What is the integral of (1/x+cot(x)-sec(x)) ?
The integral of (1/x+cot(x)-sec(x)) is ln|x|+ln|sin(x)|-ln|tan(x)+sec(x)|+C