Final answer to the problem
$x=\frac{\sqrt{e^{20}-1}}{\sqrt{10}},\:x=\frac{-\sqrt{e^{20}-1}}{\sqrt{10}}$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
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1
First, factor the terms inside the radical by $10$ for an easier handling
$\int\frac{4x}{10\left(\frac{1}{10}+x^2\right)}dx=4$
Learn how to solve problems step by step online. Solve the differential equation int((4x)/(1+10x^2))dx=4. First, factor the terms inside the radical by 10 for an easier handling. Taking the constant out of the radical. We can solve the integral \int\frac{4x}{10\left(\frac{1}{10}+x^2\right)}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above.
Final answer to the problem
$x=\frac{\sqrt{e^{20}-1}}{\sqrt{10}},\:x=\frac{-\sqrt{e^{20}-1}}{\sqrt{10}}$
