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Popular >

integral of (4/x-1)

Solution

\int (\frac{4}{x} - 1) d x

Solution

4 ln ∣ x ∣ - x + C

Solution steps

\int \frac{4}{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{4}{x} d x - \int 1 d x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int 1 d x = x

= 4 ln ∣ x ∣ - x

Add a constant to the solution

= 4 ln ∣ x ∣ - x + C

Popular Examples

(\partial)/(\partial x)(xsin(4x^2y))

\frac{\partial}{\partial x} (x sin (4 x^{2} y))

y^'=(2x)/((1+2y))

y^{^{'}} = \frac{2 x}{( 1 + 2 y )}

integral of x/(sqrt(x^4-6x^2+5))

\int \frac{x}{x ^{4} - 6 x ^{2} + 5} d x

derivative of log_{3}(x^2+1)

\frac{d}{d x} (lo g_{3} (x^{2} + 1))

derivative of (x+1/x ^2)

\frac{d}{d x} ((x + \frac{1}{x})^{2})

Frequently Asked Questions (FAQ)

What is the integral of (4/x-1) ?
The integral of (4/x-1) is 4ln|x|-x+C