What is the integral of 4/x+sec^2(x) ?

The integral of 4/x+sec^2(x) is 4ln|x|+tan(x)+C

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integral of 4/x+sec^2(x)

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

4 ln ∣ x ∣ + tan (x) + C

Solution steps

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int sec^{2} (x) d x = tan (x)

= 4 ln ∣ x ∣ + tan (x)

Add a constant to the solution

= 4 ln ∣ x ∣ + tan (x) + C

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What is the integral of 4/x+sec^2(x) ?
The integral of 4/x+sec^2(x) is 4ln|x|+tan(x)+C