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Popular Calculus >

integral of (3+1/x)

Solution

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

Solution

3 x + ln ∣ x ∣ + C

Solution steps

\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

Graph

Popular Examples

integral of sqrt(1+(-1/(x^3)+(x^3)/4)^2)

\int 1 + (- \frac{1}{x ^{3}} + \frac{x ^{3}}{4})^{2} d x

integral of (10x^2-8x-6)/(x^3-2x^2-3x)

\int \frac{10 x ^{2} - 8 x - 6}{x ^{3} - 2 x ^{2} - 3 x} d x

integral of sin^2((npix)/l)

\int sin^{2} (\frac{nπ x}{l}) d x

integral of (x^{1.5}+7x^{2.5})

\int (x^{1.5} + 7 x^{2.5}) d x

integral of (x^2)/((1+x^4))

\int \frac{x ^{2}}{( 1 + x ^{4} )} d x

Frequently Asked Questions (FAQ)

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