What is the integral of 1/(10x^3) ?

The integral of 1/(10x^3) is -1/(20x^2)+C

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integral of 1/(10x^3)

\int \frac{1}{10 x ^{3}} d x

- \frac{1}{20 x ^{2}} + C

Solution steps

\int \frac{1}{10 x ^{3}} d x

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

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

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

Simplify

\frac{1}{10} (- \frac{1}{2 x ^{2}}) : - \frac{1}{20 x ^{2}}

= - \frac{1}{20 x ^{2}}

Add a constant to the solution

= - \frac{1}{20 x ^{2}} + C

\int x^{2} 6 + x^{3} d x

\frac{d}{d r} (\frac{2}{r ^{3}})

y^{^{''}} + 10 y^{^{'}} + 41 y = 0

\int (x^{2} + 2) e^{- x} d x

n = 3 \sum \infty 4^{(n + 2)}