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Popular >

integral of x^2+1/x

Solution

\int x^{2} + \frac{1}{x} d x

Solution

\frac{x ^{3}}{3} + ln ∣ x ∣ + C

Solution steps

\int x^{2} + \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 x^{2} d x + \int \frac{1}{x} d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{3}}{3} + ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{3}}{3} + ln ∣ x ∣ + C

Popular Examples

integral of (cos(pi/(x^{17)}))/(x^{18)}

\int \frac{cos ( \frac{π}{x ^{17}} )}{x ^{18}} d x

integral of 1/(\sqrt[3]{1-2x)}

integral of ((3x-2)^2)/(sqrt(x))

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

integral of (1-x)^b

\int (1 - x)^{b} d x

integral of (x^2)/(sqrt(x-1))integral

\frac{x ^{2}}{x - 1}

Frequently Asked Questions (FAQ)

What is the integral of x^2+1/x ?
The integral of x^2+1/x is (x^3)/3+ln|x|+C