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

The integral of ((x+1)^3)/((x)^{10)} is -1/(6x^6)-3/(7x^7)-3/(8x^8)-1/(9x^9)+C

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integral of ((x+1)^3)/((x)^{10)}

\int \frac{( x + 1 ) ^{3}}{( x ) ^{10}} d x

- \frac{1}{6 x ^{6}} - \frac{3}{7 x ^{7}} - \frac{3}{8 x ^{8}} - \frac{1}{9 x ^{9}} + C

Solution steps

\int \frac{( x + 1 ) ^{3}}{x ^{10}} d x

Expand

\frac{( x + 1 ) ^{3}}{x ^{10}} : \frac{1}{x ^{7}} + \frac{3}{x ^{8}} + \frac{3}{x ^{9}} + \frac{1}{x ^{10}}

= \int \frac{1}{x ^{7}} + \frac{3}{x ^{8}} + \frac{3}{x ^{9}} + \frac{1}{x ^{10}} 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 \frac{1}{x ^{7}} d x + \int \frac{3}{x ^{8}} d x + \int \frac{3}{x ^{9}} d x + \int \frac{1}{x ^{10}} d x

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

\int \frac{3}{x ^{8}} d x = - \frac{3}{7 x ^{7}}

\int \frac{3}{x ^{9}} d x = - \frac{3}{8 x ^{8}}

\int \frac{1}{x ^{10}} d x = - \frac{1}{9 x ^{9}}

= - \frac{1}{6 x ^{6}} - \frac{3}{7 x ^{7}} - \frac{3}{8 x ^{8}} - \frac{1}{9 x ^{9}}

Add a constant to the solution

= - \frac{1}{6 x ^{6}} - \frac{3}{7 x ^{7}} - \frac{3}{8 x ^{8}} - \frac{1}{9 x ^{9}} + C

\frac{x}{99}

\frac{d}{d X} (7.1 X + 20.3)

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

\int_{0}^{3} (3 - x) x d x

\frac{d}{d y} (x (y) z (y))

What is the integral of ((x+1)^3)/((x)^{10)} ?
The integral of ((x+1)^3)/((x)^{10)} is -1/(6x^6)-3/(7x^7)-3/(8x^8)-1/(9x^9)+C