What is the antiderivative of #(2x^2 - 5)(x^2 + 1)#?

Answer 1

#(2x^5)/5-x^3-5x+C#

The question you are asking can be written as:

#int(2x^2-5)(x^2+1)dx#

First, simplify the integral by distributing the binomials.

#=int(2x^4-3x^2-5)dx#

Split this up into three separate integrals:

#=2intx^4dx-3intx^2dx-5intdx#
For the first two integrals, use the rule:#" "intx^n=x^(n+1)/(n+1)+C#
For the third, use:#" "intdx=x+C#

The multiplicative constants attached to the fronts of the integrals will just be multiplied with the rest of the antiderivatives:

Applying the rules gives:

#=2(x^5/5)-3(x^3/3)-5(x)+C#
#=(2x^5)/5-x^3-5x+C#
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Answer from HIX Tutor

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.

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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