# Integrate of [1+x+x^2]/x(1+x^2) dx = int [x+(1+x^2)]/x(1+x^2)dx, why is that rearranging of the numerator, how come?

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• Integrate of [1+x+x^2]/x(1+x^2) dx = int [x+(1+x^2)]/x(1+x^2)dx, why is that rearranging of the numerator, how come?

Integral $\int{\sqrt{25 - x^2}dx}$ ... \int{\sqrt{25 - x^2} dx} = \frac{1}{2} x\sqrt{25 ... Integrate $\int\frac{dx}{x\sqrt{x^2+x+1}}$ 4.
Positive: 93 %
To integrate 15x 4 from x = 1 to 3, enter int 15x^4 ... The definite integral of e 1/x / x 2 dx from x = 1 to ... around x = − 2 (do you understand why ...
Positive: 90 %

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keep the numerator, then split the bottom by x^3(x+1) ... x^3 + 1∫ dx /(x+1) = -3 ∫ x^(-2) dx + 3 ∫ x^(-3) dx + 1 ... How do I integrate [3/(2-x) ^2 ...
Positive: 93 %
Integrate (ln(x))^2/x^2. ... Subbing u = ln x and du = 1/x gives. ... Everything up until this point has come back to me in an "ah hah" sort of fashion.
Positive: 88 %
How to integrate the function of 3x^3/(x^3-1)? ... 1) - 3/2 / (x² + x + 1). The first of these has a numerator the ... integrate [math ... (x^3+1)(x-x^2 ...