Final answer to the problem
$\frac{1}{96}\ln\left|\frac{3}{2}+\frac{3}{4}\left(1.4142136x\right)^{2}\right|-\frac{1}{96}\ln\left|\frac{3}{2}-\frac{3}{4}\left(1.4142136x\right)^{2}\right|+C_0$
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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
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Rewrite the expression $\frac{x}{36-16x^4}$ inside the integral in factored form
$\int\frac{x}{4\left(3+2x^{2}\right)\left(3-2x^{2}\right)}dx$
Learn how to solve logarithmic equations problems step by step online.
$\int\frac{x}{4\left(3+2x^{2}\right)\left(3-2x^{2}\right)}dx$
Learn how to solve logarithmic equations problems step by step online. Find the integral int(x/(36-16x^4))dx. Rewrite the expression \frac{x}{36-16x^4} inside the integral in factored form. Take the constant \frac{1}{4} out of the integral. Rewrite the fraction \frac{x}{\left(3+2x^{2}\right)\left(3-2x^{2}\right)} in 2 simpler fractions using partial fraction decomposition. Simplify the expression.
Final answer to the problem
$\frac{1}{96}\ln\left|\frac{3}{2}+\frac{3}{4}\left(1.4142136x\right)^{2}\right|-\frac{1}{96}\ln\left|\frac{3}{2}-\frac{3}{4}\left(1.4142136x\right)^{2}\right|+C_0$
