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Integrate the function $\frac{x^3-6x-20}{x+5}$ from $1$ to $2$

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Final Answer

$-3.893995$
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Step-by-step Solution

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Divide $x^3-6x-20$ by $x+5$

$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}x^{2}-5x\phantom{;}+19\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-6x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-x^{3}-5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-5x^{2};}-5x^{2}-6x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}5x^{2}+25x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{2}+25x\phantom{;}-;x^n;}\phantom{;}19x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-19x\phantom{;}-95\phantom{;}\phantom{;}}\\\phantom{;;-19x\phantom{;}-95\phantom{;}\phantom{;}-;x^n-;x^n;}-115\phantom{;}\phantom{;}\\\end{array}$

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$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}x^{2}-5x\phantom{;}+19\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-6x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-x^{3}-5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-5x^{2};}-5x^{2}-6x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}5x^{2}+25x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{2}+25x\phantom{;}-;x^n;}\phantom{;}19x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-19x\phantom{;}-95\phantom{;}\phantom{;}}\\\phantom{;;-19x\phantom{;}-95\phantom{;}\phantom{;}-;x^n-;x^n;}-115\phantom{;}\phantom{;}\\\end{array}$

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Learn how to solve problems step by step online. Integrate the function (x^3-6x+-20)/(x+5) from 1 to 2. Divide x^3-6x-20 by x+5. Resulting polynomial. Expand the integral \int_{1}^{2}\left(x^{2}-5x+19+\frac{-115}{x+5}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{1}^{2} x^{2}dx results in: \frac{7}{3}.

Final Answer

$-3.893995$

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Function Plot

Plotting: $\frac{x^3-6x-20}{x+5}$

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a
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n
u
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x
y
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.
(◻)
+
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◻/◻
/
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2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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