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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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Take out the constant $8$ from the integral
Learn how to solve improper integrals problems step by step online.
$8\int\frac{\arctan\left(4y\right)}{1+16y^2}dy$
Learn how to solve improper integrals problems step by step online. Integrate the function (8arctan(4y))/(1+16y^2) from 0 to infinity. Take out the constant 8 from the integral. We can solve the integral \int\frac{\arctan\left(4y\right)}{1+16y^2}dy by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 4y it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dy in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dy in the previous equation.
