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Popular >

integral of-(x+1)/x

Solution

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

Solution

- x - ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Expand

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

= - \int 1 + \frac{1}{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{1}{x} d x)

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= - (x + ln ∣ x ∣)

Simplify

= - x - ln ∣ x ∣

Add a constant to the solution

= - x - ln ∣ x ∣ + C

Popular Examples

4y^{''}-4y^'-3y=0

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0

implicit (dy)/(dx),y^2=2x implicit derivative

\frac{d y}{d x}, y^{2} = 2 x

derivative of 10x^3

\frac{d}{d x} (10 x^{3})

integral of sqrt(a^2-r^2)r

\int a^{2} - r^{2} r d r

(\partial)/(\partial x)(10x+4y)

\frac{\partial}{\partial x} (10 x + 4 y)

Frequently Asked Questions (FAQ)

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