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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

Graph

Popular Examples

derivative of ln(2)x^5 derivative of

ln (2) x^{5}

integral of x^5sqrt(11+x^6)

\int x^{5} 11 + x^{6} d x

integral of u/(1+u^2)

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

limit as x approaches ln(2) of e^{2x}

x \to l n (2) lim (e^{2 x})

inverse oflaplace 1/((s+65))inverse laplace

\frac{1}{( s + 65 )}

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