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TheTimeTraveler
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Member warned about posting homework questions in a technical forum section
∫(x+1)/(x^2 + 4x +5) dx
Anyone can help me doing it using Arctan and ln
Anyone can help me doing it using Arctan and ln
∫(x+1)/(x^2+4x+5) dx = 1/2∫ (2x+2)/(x^2+4x+5) dx = 1/2∫(2x+4)/(x^2+4x+5) dx + 1/2∫(-2)/(1+(x+2)^2) dxblue_leaf77 said:Let's first hear out your own idea to solve this problem? What strategy you have in mind?
ThaanksHallsofIvy said:Don't forget the "constant of integration".
The formula for finding the integral of (x+1)/(x^2+4x+5) is ∫(x+1)/(x^2+4x+5)dx = ln(x^2+4x+5) + C, where C is the constant of integration.
To solve the integral of (x+1)/(x^2+4x+5), you can use the substitution method by letting u = x^2+4x+5 and du = (2x+4)dx. This will result in the integral becoming ∫(1/u)du = ln(u) + C = ln(x^2+4x+5) + C.
No, the power rule cannot be used to find the integral of (x+1)/(x^2+4x+5) because the power rule is only applicable for integrals with the form ∫x^n dx.
The domain of the function (x+1)/(x^2+4x+5) is all real numbers except for x = -5 and x = -1, as these values would result in a division by zero.
No, the integral of (x+1)/(x^2+4x+5) is not always positive. It will result in a positive value if the lower limit is less than the upper limit, but it can also be negative if the lower limit is greater than the upper limit.