Simplify the following rational expression. State the domain restrictions: a) x3-8 2x3-8a

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A: I=∫x7x4+1dxI=∫x4(x4+1)x3dxI=14∫x4(x4+1)4x3dxSubstitute x4+1=u

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A: To evaluate the following integral by interpreting in terms of areas.

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A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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A: y=x2−x+10 at x=10dydx=ddxx2−x+10Chain Ruleddxf(g(x))=f′(g(x))g′(x)Using the power Ruleddxxn=nxn−1

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A: x=t7+1,y=t8+t;t=−1x(−1)=−1+1=0y(−1)=1−1=0(x0,y0)=(0,0)Using the power Ruleddxxn=nxn−1

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A: Let .To find .

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A: To calculate the following integral.

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Q: EASE could you shed a litttle bit more light on how you got the critical numbers

A: So, f'(x)=0 gives us