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Popular >

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

Popular Examples

limit as x approaches 0 of 2x+12

x \to 0 lim (2 x + 12)

derivative of ln(sec^2(x))derivative of

ln (sec^{2} (x))

y^{''}+16y=2sec(4x)

y^{^{''}} + 16 y = 2 sec (4 x)

limit as x approaches 7 of-x^2+x-7

x \to 7 lim (- x^{2} + x - 7)

integral of 1/(T-70)

\int \frac{1}{T - 70} d T

Frequently Asked Questions (FAQ)

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