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Popular Calculus >

integral of 1/(5x^3)

Solution

\int \frac{1}{5 x ^{3}} d x

Solution

- \frac{1}{10 x ^{2}} + C

Solution steps

\int \frac{1}{5 x ^{3}} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

= \frac{1}{5} (- \frac{1}{2 x ^{2}})

Simplify

\frac{1}{5} (- \frac{1}{2 x ^{2}}) : - \frac{1}{10 x ^{2}}

= - \frac{1}{10 x ^{2}}

Add a constant to the solution

= - \frac{1}{10 x ^{2}} + C

Graph

Popular Examples

tangent of f(x)=x^4-20x^2+64,\at x=-2

t an g e n t f (x) = x^{4} - 20 x^{2} + 64, at x = - 2

factor 24x^3+24x^2

f a c t or 24 x^{3} + 24 x^{2}

derivative of 2x^2-1/(x^2+1/(x^3))

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

integral of (31)/(x^3-27)

\int \frac{31}{x ^{3} - 27} d x

(\partial)/(\partial y)(6x^{y/z})

\frac{\partial}{\partial y} (6 x^{\frac{y}{z}})

Frequently Asked Questions (FAQ)

What is the integral of 1/(5x^3) ?
The integral of 1/(5x^3) is -1/(10x^2)+C