Final answer to the problem
$\frac{1}{2}x\sqrt{1+4x^2}+\frac{1}{4}\ln\left|\sqrt{1+4x^2}+2x\right|+C_0$
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Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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1
First, factor the terms inside the radical by $4$ for an easier handling
$\int\sqrt{4\left(\frac{1}{4}+x^2\right)}dx$
Learn how to solve logarithmic differentiation problems step by step online.
$\int\sqrt{4\left(\frac{1}{4}+x^2\right)}dx$
Learn how to solve logarithmic differentiation problems step by step online. Integrate int((1+4x^2)^(1/2))dx. First, factor the terms inside the radical by 4 for an easier handling. Taking the constant out of the radical. We can solve the integral \int2\sqrt{\frac{1}{4}+x^2}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
$\frac{1}{2}x\sqrt{1+4x^2}+\frac{1}{4}\ln\left|\sqrt{1+4x^2}+2x\right|+C_0$
