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Popular >

integral of (x^3)/3*1/x

Solution

\int \frac{x ^{3}}{3} \cdot \frac{1}{x} d x

Solution

\frac{x ^{3}}{9} + C

Solution steps

\int \frac{x ^{3}}{3} \cdot \frac{1}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int x^{3} \frac{1}{x} d x

Simplify

x^{3} \frac{1}{x} : x^{2}

= \frac{1}{3} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{3} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{3} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{9}

= \frac{x ^{3}}{9}

Add a constant to the solution

= \frac{x ^{3}}{9} + C

Popular Examples

integral of (-ln(x))/(x^2)

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

derivative of sqrt(3+y^2)derivative of

3 + y^{2}

y^{''}-2y^'=(4t+9)sin(2t)

y^{^{''}} - 2 y^{^{'}} = (4 t + 9) sin (2 t)

integral of 2sec^2(x)

\int 2 sec^{2} (x) d x

integral from-1 to 0 of 1/x

\int_{- 1}^{0} \frac{1}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (x^3)/3*1/x ?
The integral of (x^3)/3*1/x is (x^3)/9+C