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Popular >

integral of (2x+1)/x

Solution

\int \frac{2 x + 1}{x} d x

Solution

2 x + ln ∣ x ∣ + C

Solution steps

\int \frac{2 x + 1}{x} d x

Expand

\frac{2 x + 1}{x} : 2 + \frac{1}{x}

= \int 2 + \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 2 d x + \int \frac{1}{x} d x

\int 2 d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x + ln ∣ x ∣

Add a constant to the solution

= 2 x + ln ∣ x ∣ + C

Popular Examples

(\partial)/(\partial y)(2xy-6y)

\frac{\partial}{\partial y} (2 x y - 6 y)

integral of e^{-1/x}

\int e^{- \frac{1}{x}} d x

(\partial)/(\partial x)(f(x,y)(x+y))

\frac{\partial}{\partial x} (f (x, y) (x + y))

integral from 0 to 1 of (r^3)/(4+r^2)

\int_{0}^{1} \frac{r ^{3}}{4 + r ^{2}} d r

limit as x approaches 2 of (5-x)/(x-2)

x \to 2 lim (\frac{5 - x}{x - 2})

Frequently Asked Questions (FAQ)

What is the integral of (2x+1)/x ?
The integral of (2x+1)/x is 2x+ln|x|+C