
Evaluate the following integral. X2 + 16x-4 S*** dx x2 - 4x Find the partial fraction decomposition of the integrand. 1 * +18 x2 + 16x-4 dx = x² - 4x JOdx Evaluate the indefinite integral. *x? + 16x-4 dx = 3 х - 4x
Find the following integral. S* х 6x + 1 dx 6x + 1 dx =
calculate integral 5x3 + 8x2 + 15x + 8 (x2 + 1)(x2 + 3) dx
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Evaluate the following integral. jungle In? (x²) -dx s in? (x2) -dx = (Type an integer or a simplified fraction.) X h
(2) Calculate the following integrals: х 2.x3 – 4x + 3 -dx (x + 1)2(x2 +1) Java 2 - 25 2 dx x4V x2 – 25 (3) Explain why, using the techniques we've learned so far, we are able to calculate the integral of any rational function. (A rational function is one of the form p(x) where g(x2) p and q are polynomials.)
Evaluate the following integral.. 5e 6Inx -dx х Soon 1 5 e 6'nx dx = (Type an exact answer.) Х 1
(1 point) Consider the integral - 5x dx 1 + x2 If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral. (1 point) Determine whether the sequence {V17n + 14 - V17n} converges or diverges. If it converges, find the limit. Converges (y/n): Limit (if it exists, blank otherwise): (1 point) Find the limit of the sequence: 1n+ 9n + 8 an 2n2 + 3n + 8 =
Evaluate the following integral using trigonometric substitution. dx s 3 2 (529 + x2) dx 3 2 (529 +x2) (Type an exact answer.)
Evaluate the following integral or state that it diverges. 00 dx S x2 + 256 - 00 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. dx ОА. s (Type an exact answer, using * as needed.) + 256 OB. The improper integral diverges.
Consider the integral le -5x 1 + x2 dx If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral.