Final answer to the problem
$\frac{3e\sqrt{5+x}\left(1+\sqrt{5-x}\right)}{-4+x}$
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Step-by-step Solution
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- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
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1
Multiply and divide the fraction $\frac{3e\sqrt{5+x}}{1-\sqrt{5-x}}$ by the conjugate of it's denominator $1-\sqrt{5-x}$
$\frac{3e\sqrt{5+x}}{1-\sqrt{5-x}}\frac{1+\sqrt{5-x}}{1+\sqrt{5-x}}$
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$\frac{3e\sqrt{5+x}}{1-\sqrt{5-x}}\frac{1+\sqrt{5-x}}{1+\sqrt{5-x}}$
Learn how to solve rationalisation problems step by step online. Rationalize and simplify the expression (3*e(5+x)^(1/2))/(1-(5-x)^(1/2)). Multiply and divide the fraction \frac{3e\sqrt{5+x}}{1-\sqrt{5-x}} by the conjugate of it's denominator 1-\sqrt{5-x}. Multiplying fractions \frac{3e\sqrt{5+x}}{1-\sqrt{5-x}} \times \frac{1+\sqrt{5-x}}{1+\sqrt{5-x}}. Solve the product of difference of squares \left(1-\sqrt{5-x}\right)\left(1+\sqrt{5-x}\right).
Final answer to the problem
$\frac{3e\sqrt{5+x}\left(1+\sqrt{5-x}\right)}{-4+x}$
