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Popular >

integral of 1/x+1

Solution

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

Solution

ln ∣ x ∣ + x + C

Solution steps

\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 \sqrt[3]{r^2}

\int 3 r^{2} d r

tangent of f(x)=x^2+5,\at x=2 tangent of

f (x) = x^{2} + 5, at x = 2

tangent of y=x^3-4x,(2,0)tangent of

y = x^{3} - 4 x, (2, 0)

y^{''}+25y=-30sin(5t)

y^{^{''}} + 25 y = - 30 sin (5 t)

integral from 2 to 4 of 1/((x-1)(x-4))

\int_{2}^{4} \frac{1}{( x - 1 ) ( x - 4 )} d x

Frequently Asked Questions (FAQ)

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