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Popular Calculus >

integral of (1+x)/x

Solution

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

Solution

ln ∣ x ∣ + x + C

Solution steps

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

Expand

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int 1 d x = x

= ln ∣ x ∣ + x

Add a constant to the solution

= ln ∣ x ∣ + x + C

Graph

Popular Examples

derivative of 5x^4(9-7x)^7

d er i v a t i v e 5 x^{4} (9 - 7 x)^{7}

integral from-pi to pi of 1

\int_{- π}^{π} 1

tangent of f(x)=x^3-3x^2-8x+9

t an g e n t f (x) = x^{3} - 3 x^{2} - 8 x + 9

limit as x approaches infinity of 5+2/x

x \to \infty lim (5 + \frac{2}{x})

sec^2(x)dy+csc(y)dx=0,y(pi/4)=0

sec^{2} (x) d y + csc (y) d x = 0, y (\frac{π}{4}) = 0

Frequently Asked Questions (FAQ)

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