Final answer to the problem
The integral diverges.
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
Take out the constant $t$ from the integral
$t\int\frac{x\arctan\left(x\right)}{\left(1+x^2\right)^2}dx$
Learn how to solve definite integrals problems step by step online.
$t\int\frac{x\arctan\left(x\right)}{\left(1+x^2\right)^2}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (xtarctan(x))/((1+x^2)^2) from 0 to infinity. Take out the constant t from the integral. Expand the expression \left(1+x^2\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. We can factor the fourth degree trinomial 1+2x^2+x^{4} by applying the substitution: y=x^2. The trinomial y^2+2y+1 is a perfect square trinomial, because it's discriminant is equal to zero.
Final answer to the problem
The integral diverges.
