Final answer to the problem
The integral diverges.
Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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- Weierstrass Substitution
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- Product of Binomials with Common Term
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1
Expand the expression $\left(x^2+25\right)^2$ using the square of a binomial: $(a+b)^2=a^2+2ab+b^2$
Learn how to solve improper integrals problems step by step online.
$\int\frac{x^2\cos\left(\frac{x}{5}\right)}{x^{4}+50x^2+625}dx$
Learn how to solve improper integrals problems step by step online. Integrate the function (x^2cos(x/5))/((x^2+25)^2) from 0 to infinity. Expand the expression \left(x^2+25\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. We can factor the fourth degree trinomial x^{4}+50x^2+625 by applying the substitution: y=x^2. The trinomial y^2+50y+625 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula.
Final answer to the problem
The integral diverges.
