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Popular >

integral of (3x+1)/x

Solution

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

Solution

3 x + ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{3 x + 1}{x} : 3 + \frac{1}{x}

= \int 3 + \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 3 d x + \int \frac{1}{x} d x

\int 3 d x = 3 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 3 x + ln ∣ x ∣

Add a constant to the solution

= 3 x + ln ∣ x ∣ + C

Popular Examples

y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=0

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = 0

derivative of 2x^2+7

\frac{d}{d x} (2 x^{2} + 7)

tangent of f(x)=(4x+5)(5x-1),\at x=3 tangent of

f (x) = (4 x + 5) (5 x - 1), at x = 3

integral of 25e^{-5x}sin(5x)

\int 25 e^{- 5 x} sin (5 x) d x

integral of-x/(sqrt(1-x^2))

\int - \frac{x}{1 - x ^{2}} d x

Frequently Asked Questions (FAQ)

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