Find the integral: ∫ e x 9 − 4 e 2 x d x.

Simplify the denominator.ex(3+2ex)(3-2ex)Multiply&nbsp;ex(3+2ex)(3-2ex)&nbsp;by&nbsp;(3+2ex)(3-2ex)(3+2ex)(3-2ex).ex(3+2ex)(3-2ex)⋅(3+2ex)(3-2ex)(3+2ex)(3-2ex)Combine and simplify the denominator.ex(3+2ex)(3-2ex)(3+2ex)(3-2ex)&nbsp;

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College
Calculus and Analysis
Integral Calculus
Integrals

Jay Barrett

Answered question

2022-05-13

Find the integral:

\int \frac{e^{x}}{\sqrt{9 - 4 e^{2 x}}} d x

Answer & Explanation

Elliana Shelton

Beginner2022-05-14Added 14 answers

Simplify the denominator.

$\frac{e^{x}}{\sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}}$

Multiply $\frac{e^{x}}{\sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}}$ by $\frac{\sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}}{\sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}}$ .

$\frac{e^{x}}{\sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}} \cdot \frac{\sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}}{\sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}}$

Combine and simplify the denominator.

$\frac{e^{x} \sqrt{(3 + 2 e^{x}) (3 - 2 e^{x})}}{(3 + 2 e^{x}) (3 - 2 e^{x})}$

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