What is the integral of tan(x)+1/x ?

The integral of tan(x)+1/x is -ln|cos(x)|+ln|x|+C

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integral of tan(x)+1/x

integral

tan (x) + \frac{1}{x}

- ln ∣ cos (x) ∣ + ln ∣ x ∣ + C

Solution steps

\int tan (x) + \frac{1}{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 tan (x) d x + \int \frac{1}{x} d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int \frac{1}{x} d x = ln ∣ x ∣

= - ln ∣ cos (x) ∣ + ln ∣ x ∣

Add a constant to the solution

= - ln ∣ cos (x) ∣ + ln ∣ x ∣ + C

e^{\frac{- y}{2}}

\frac{e ^{2} x}{2}

1 - tan^{2} (x)

\frac{x ^{3}}{( x + 2 ) ^{4}}

x^{3} (x^{2} + 4)^{\frac{1}{2}}

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