How do you find the indefinite integral of #int -24x^5 dx#?

Answer 1

#int-24x^5dx=-4x^6+C#

Use the rule #intaf(x)dx=aintf(x)dx# to move the constant out of the integral.
#int-24x^5dx=-24intx^5dx#
Now use this integral rule, which is the opposite of the power rule for differentiation, to integrate the remaining term: #intx^ndx=x^(n+1)/(n+1)+C#
#-24intx^5dx=-24(x^(5+1)/(5+1))+C=-24/6x^6+C=-4x^6+C#
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Answer 2

To find the indefinite integral of ( \int -24x^5 , dx ), you can use the power rule for integration. According to the power rule, the integral of ( x^n ) with respect to ( x ) is ( \frac{{x^{n+1}}}{{n+1}} + C ), where ( n ) is any real number except -1 and ( C ) is the constant of integration. Applying this rule to ( -24x^5 ), you get:

[ \int -24x^5 , dx = -\frac{{24x^{5+1}}}{{5+1}} + C = -\frac{{24x^6}}{6} + C = -4x^6 + C ]

So, the indefinite integral of ( -24x^5 , dx ) is ( -4x^6 + C ), where ( C ) is the constant of integration.

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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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