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Popular >

integral of 3/x-1

Solution

\int \frac{3}{x} - 1 d x

Solution

3 ln ∣ x ∣ - x + C

Solution steps

\int \frac{3}{x} - 1 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{3}{x} d x - \int 1 d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 1 d x = x

= 3 ln ∣ x ∣ - x

Add a constant to the solution

= 3 ln ∣ x ∣ - x + C

Graph

Popular Examples

integral of (sin(30x))/(1+cos^2(30x))

\int \frac{sin ( 30 x )}{1 + cos ^{2} ( 30 x )} d x

integral of 1/2 sec(x)

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

integral of (e^{2x}+e^{5x})/(e^{3x)}

\int \frac{e ^{2 x} + e ^{5 x}}{e ^{3 x}} d x

integral of 2x(x^2+10)^4

\int 2 x (x^{2} + 10)^{4} d x

integral of x^3cos(x^4+3)

\int x^{3} cos (x^{4} + 3) d x

Frequently Asked Questions (FAQ)

What is the integral of 3/x-1 ?
The integral of 3/x-1 is 3ln|x|-x+C