The following integral requires a preliminary step such as long division or a change of variables before using the method of partial fractions. Evaluate the following integral. x^4 + 7/x^3 + 2x dx Find the partial fraction decomposition of the integrand. x^4 + 7/x^3 + 2x dx

Division yields

Now for partial fractions: you're looking for constants a, b, and c such that

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

Now, in the integral we get

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

step-by-step explanation:

. your answer will contain x - and y -terms. (1 point) x ( ¿¿ 2 − 7 ) 2 +( y 2 − 9 ) 2 √ ¿ 12. what is the distance from the directrix (the crocodile river) to the point ( x , y )? write this equation. your answer will contain a y -term.

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step-by-step explanation: