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Popular Calculus >

integral of 6/(x^3)

Solution

\int \frac{6}{x ^{3}} d x

Solution

- \frac{3}{x ^{2}} + C

Solution steps

\int \frac{6}{x ^{3}} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

= 6 (- \frac{1}{2 x ^{2}})

Simplify

6 (- \frac{1}{2 x ^{2}}) : - \frac{3}{x ^{2}}

= - \frac{3}{x ^{2}}

Add a constant to the solution

= - \frac{3}{x ^{2}} + C

Graph

Popular Examples

integral from-1 to 1 of t^3(4+t^4)^3

\int_{- 1}^{1} t^{3} (4 + t^{4})^{3} d t

integral of (x^2-x+2)/(3x^3-2x^2+6x-4)

\int \frac{x ^{2} - x + 2}{3 x ^{3} - 2 x ^{2} + 6 x - 4} d x

area y=(x^2)/2+2,[-3,0]

a re a y = \frac{x ^{2}}{2} + 2, [- 3, 0]

derivative of (3x+6^2)

\frac{d}{d x} ((3 x + 6)^{2})

area y=-x^2-2x+3,y=-x+1

a re a y = - x^{2} - 2 x + 3, y = - x + 1

Frequently Asked Questions (FAQ)

What is the integral of 6/(x^3) ?
The integral of 6/(x^3) is -3/(x^2)+C