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Popular >

integral of (1+2x)/x

Solution

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

Solution

ln ∣ x ∣ + 2 x + C

Solution steps

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

Expand

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int 2 d x = 2 x

= ln ∣ x ∣ + 2 x

Add a constant to the solution

= ln ∣ x ∣ + 2 x + C

Popular Examples

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n \to \infty lim (3)

(\partial)/(\partial x)(cos(ye^{xy})sin(x))

\frac{\partial}{\partial x} (cos (y e^{x y}) sin (x))

integral of ((a^2-x^2)^{3/2})/(x^4)

\int \frac{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}}{x ^{4}} d x

limit as x approaches 0 of (sin(16x))/(3x)

x \to 0 lim (\frac{sin ( 16 x )}{3 x})

integral of 3^{2x}

\int 3^{2 x} d x

Frequently Asked Questions (FAQ)

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