What is the integral of (5/x+sec^2(x)) ?

The integral of (5/x+sec^2(x)) is 5ln|x|+tan(x)+C

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integral of (5/x+sec^2(x))

\int (\frac{5}{x} + sec^{2} (x)) d x

5 ln ∣ x ∣ + tan (x) + C

Solution steps

\int \frac{5}{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{5}{x} d x + \int sec^{2} (x) d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ + tan (x)

Add a constant to the solution

= 5 ln ∣ x ∣ + tan (x) + C

x \to 2 lim (3.5 + 5.6)

x \to 2 - lim (\frac{2 - ∣ x ∣}{2 + x})

(4 x + 3)^{5}

y^{^{''}} - 3 y^{^{'}} - 4 y = 6 e^{2 t}

x \to 0 + lim (\frac{3 x e ^{2 x}}{sin ( 6 x )})

What is the integral of (5/x+sec^2(x)) ?
The integral of (5/x+sec^2(x)) is 5ln|x|+tan(x)+C