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Show that the integral of a quotient is not the quotient of the integrals by carrying out the following steps: (Use â‚¬ for the constant = 0)

(a) Find the integral of the quotient shown below by evaluating âˆ«(X+C) dx:

(b) Find the corresponding quotient of the integrals shown below. (Do not simplify your answer)

âˆ«(3* dx) / âˆ«(3x dx)

Do the answers for parts (a) and (b) agree?

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02:59

Calculate the integrals by partial fractions and then by using the indicated substitution. Show that the results you get are the same.$$\int \frac{3 x^{2}+1}{x^{3}+x} d x ; \text { substitution } w=x^{3}+x$$

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01:49

(a) Use the Endpaper Integral Table to evaluate the given integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a).$$\int x \sqrt{2 x+3} d x$$

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Transcript

in this problem we are asked to show that the integral of a cautioned is not equal to the caution of the integral. So in order to show this, we first evaluate the integral of three times x over three times x dx. In order to evaluate this, we simplify the integration three times x and three times x get canceled. So we have integral of dx and we know that the integral of exp r zero times dx is equivalent to integral of dx the anti derivative of experts in yes exp R n plus one divided by N plus one. Here we have explored zero. So we get x par zero plus one which is one divided by one plus the constant of integration C. So we had X plus the constant of integration C. So this is the answer for integral of ctx Over three X DX. Next let us evaluate the integral of three x dx or worse? The integral of three times x dx. So we see that the integral of three X dx equals two three times. Using the same anti derivative formula we get ex parte one plus one which is two over to Plus the…

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