# How do you integrate #x^3/(x^2+2x+1)# using partial fractions?

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Though the Problem is requred to be solved using Partial Fractions,

as a Second Method, we show that the same can be solved

easily without its use.

Enjoy Maths.!

Respected Shwetank Mauria has derived!

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To integrate ( \frac{x^3}{x^2 + 2x + 1} ) using partial fractions, first factor the denominator, which is ( (x + 1)^2 ). Then, express the fraction as ( \frac{A}{x+1} + \frac{B}{(x+1)^2} ). After finding the values of ( A ) and ( B ), integrate each term separately. The integral of ( \frac{A}{x+1} ) can be found using the natural logarithm, and the integral of ( \frac{B}{(x+1)^2} ) can be found using reverse power rule.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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