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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

Graph

Popular Examples

integral of 2sin^2(x/2)

\int 2 sin^{2} (\frac{x}{2}) d x

integral of 1/(cos(x)-sin(x))

\int \frac{1}{cos ( x ) - sin ( x )} d x

integral of tan^5(θ)

\int tan^{5} (θ) d θ

integral of Q^2-4Q+10

\int Q^{2} - 4 Q + 10 d Q

integral of 1/(v+1)

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

Frequently Asked Questions (FAQ)

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