What is the integral of (2x-3)/(x^26x^{13)} ?

The integral of (2x-3)/(x^26x^{13)} is 1/6 (-2/(13x^{13)}+3/(14x^{14)})+C

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integral of (2x-3)/(x^26x^{13)}

\int \frac{2 x - 3}{x ^{2} 6 x ^{13}} d x

\frac{1}{6} (- \frac{2}{13 x ^{13}} + \frac{3}{14 x ^{14}}) + C

Solution steps

\int \frac{2 x - 3}{x ^{2} \cdot 6 x ^{13}} d x

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{2 x - 3}{x ^{2} x ^{13}} d x

Expand

\frac{2 x - 3}{x ^{2} x ^{13}} : \frac{2}{x ^{14}} - \frac{3}{x ^{15}}

= \frac{1}{6} \cdot \int \frac{2}{x ^{14}} - \frac{3}{x ^{15}} 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

= \frac{1}{6} (\int \frac{2}{x ^{14}} d x - \int \frac{3}{x ^{15}} d x)

\int \frac{2}{x ^{14}} d x = - \frac{2}{13 x ^{13}}

\int \frac{3}{x ^{15}} d x = - \frac{3}{14 x ^{14}}

= \frac{1}{6} (- \frac{2}{13 x ^{13}} - (- \frac{3}{14 x ^{14}}))

Simplify

= \frac{1}{6} (- \frac{2}{13 x ^{13}} + \frac{3}{14 x ^{14}})

Add a constant to the solution

= \frac{1}{6} (- \frac{2}{13 x ^{13}} + \frac{3}{14 x ^{14}}) + C

\int \frac{e ^{2 x}}{e ^{x} + 1} d x

x \to 0 lim (\frac{( x + 2 ) ^{2} - 8}{x})

x^{2} + 8 x - 3, - x^{2} + 4 x + 3

n = 1 \sum \infty \frac{5 ^{n}}{9}

f (x) = \frac{sin ( 4 x )}{sin ( 5 x )}

What is the integral of (2x-3)/(x^26x^{13)} ?
The integral of (2x-3)/(x^26x^{13)} is 1/6 (-2/(13x^{13)}+3/(14x^{14)})+C