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Popular >

integral of (x-7)/x

Solution

\int \frac{x - 7}{x} d x

Solution

x - 7 ln ∣ x ∣ + C

Solution steps

\int \frac{x - 7}{x} d x

Expand

\frac{x - 7}{x} : 1 - \frac{7}{x}

= \int 1 - \frac{7}{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 1 d x - \int \frac{7}{x} d x

\int 1 d x = x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= x - 7 ln ∣ x ∣

Add a constant to the solution

= x - 7 ln ∣ x ∣ + C

Popular Examples

integral of 3/x x^2

\int \frac{3}{x} x^{2} d x

integral of sqrt(1+8t^2)

\int 1 + 8 t^{2} d t

integral of x^2*sqrt(4-x^3)

\int x^{2} \cdot 4 - x^{3} d x

integral of (sec(x))/(sec(x)+2tan(x)-1)

\int \frac{sec ( x )}{sec ( x ) + 2 tan ( x ) - 1} d x

integral of ()/(2u)

\int \frac{d u}{2 u} d x

Frequently Asked Questions (FAQ)

What is the integral of (x-7)/x ?
The integral of (x-7)/x is x-7ln|x|+C