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

x y^{^{'}} + y = e^{x}, y (1) = 8

cos^{2} (5 π x)

\frac{5 ln ( 4 x )}{2 - 3 x}

\int \frac{4}{5} - \frac{8}{x} d x

\int \frac{π}{200} sin (\frac{π x}{100}) d x

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