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 1 lim (\frac{- 3 x}{x - 1})

v^{'} = v^{2}

x \to 2 lim (2 x^{2})

\frac{d x}{d t} = - x (x + 2), x (0) = 1

\frac{\partial}{\partial y} (x e^{y 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