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How do you integrate #int (-9/x^4)dx#?

Answer 1

Samantha Adkison

The answer is #=3/x^3+C#

We need

#intx^ndx=x^(n+1)/(n+1)+C(n!=-1)#

Here,

#int-9/x^4dx=-9intx^-4dx#

#=-9x^(-4+1)/(-4+1)+C#

#=-9/-3*1/x^3*C#

#=3/x^3+C#

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Answer 2

Isabella Ackerman

To integrate ( \int \frac{-9}{x^4} , dx ), you can use the power rule for integration. The integral of ( x^n ) is ( \frac{x^{n+1}}{n+1} ), where ( n ) is not equal to -1. Apply this rule to the given integral by adding 1 to the exponent and dividing by the new exponent:

[ \int \frac{-9}{x^4} , dx = -9 \int x^{-4} , dx ]

[ = -9 \left( \frac{x^{-4+1}}{-4+1} \right) + C ]

[ = -9 \left( \frac{x^{-3}}{-3} \right) + C ]

[ = \frac{9}{3x^3} + C ]

[ = \frac{3}{x^3} + C ]

So, ( \int \frac{-9}{x^4} , dx = \frac{3}{x^3} + 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.