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Popular >

integral of (1+13x)/x

Solution

\int \frac{1 + 13 x}{x} d x

Solution

ln ∣ x ∣ + 13 x + C

Solution steps

\int \frac{1 + 13 x}{x} d x

Expand

\frac{1 + 13 x}{x} : \frac{1}{x} + 13

= \int \frac{1}{x} + 13 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{1}{x} d x + \int 13 d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int 13 d x = 13 x

= ln ∣ x ∣ + 13 x

Add a constant to the solution

= ln ∣ x ∣ + 13 x + C

Popular Examples

x \cdot y \cdot y^{^{'}} = y^{2} + 1

integral of-18x^2

\int - 18 x^{2} d x

limit as x approaches 2-of x/(x-2)

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

derivative of y=5x^2+7x-4 derivative of

y = 5 x^{2} + 7 x - 4

derivative of 4^{4x}derivative of

4^{4 x}

Frequently Asked Questions (FAQ)

What is the integral of (1+13x)/x ?
The integral of (1+13x)/x is ln|x|+13x+C