Consider the given expression, #10; #10; ⇒5x( #10;x+1 )( x^2 4 ) #10; #10; ⇒5x( #10;x^3 4x+x^2 4 ) #10; #10; ⇒5xx^3+x^2 4x 4 #10 ...

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Definite Integral as Limit of Sum

Solve: 5x/x+...

Question

Solve:
$\frac{5 x}{(x + 1) (x^{2} - 4)} .$

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Solution

Consider the given expression,

$\Rightarrow \frac{5 x}{(x + 1) (x^{2} - 4)}$

$\Rightarrow \frac{5 x}{(x^{3} - 4 x + x^{2} - 4)}$

$\Rightarrow \frac{5 x}{x^{3} + x^{2} - 4 x - 4}$

Hence, this is the answer.

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\frac{5 x}{(x + 1) (x^{2} - 4)}

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} - 1 & x^{2} + 2 x + 1 & 2 x^{2} + 3 x + 1 2 x^{2} + x - 1 & 2 x^{2} + 5 x - 3 & 4 x^{2} + 4 x - 3 6 x^{2} - x - 2 & 6 x^{2} - 7 x + 2 & 12 x^{2} - 5 x - 2 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

{({tan}^{- 1} x)}^{2} + {({cos}^{- 1} x)}^{2} = \frac{5 π^{2}}{8}

\frac{(2 - x^{2}) (x - 3)^{3}}{(x + 1) (x^{2} - 3 x - 4)} ⩾ 0

\int \frac{5 x}{(x + 1) (x^{2} - 4)} d x

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