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One of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate with the part that can be done with the Power Rule, and explain why the Power Rule cannot be used to evaluate the other.(a) 5(6+5x)^10dx(b) 14x^2(2x^7+9)^6dx

Question

One of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate with the part that can be done with the Power Rule, and explain why the Power Rule cannot be used to evaluate the other.

(a) 5(6+5x)^10dx

(b) 14x^2(2x^7+9)^6dx

check_circleAnswer
Step 1

(a) can be integrated using power rule. 

(b) can not be integrated using power rule because (b) has two parts of x. And we can not substitute using only variable to apply power rule. 

Step 2

First assume z=6+5x ...

Assume z=6+5x
dz=5dx
dz
dx=
5
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Assume z=6+5x dz=5dx dz dx= 5

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Calculus

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