Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5)...
Express the integrand as a sum of partial fractions and evaluate the integral. 48x2 s dx (x-24)(x+8)2 Express the integrand as a sum of partial fractions. S 48x? dx= (x - 24)(x+8)2 SO dx Evaluate the indefinite integral. 48x? (x - 24)(x + 8)2 dx =
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
Evaluate the following integral using trigonometric substitution. 7x² dx (121 + x2) 7x² dx s (121 +x?)? (Type an exact answer.)
2. Integrate by parts S x2 e e-* dx . 3. Use the method of partial fractions to evaluate S ( 5x-5 3x2-8x-3
Answer is B, please show and explain steps Thank you Express the integrand as a sum of partial fractions and evaluate the integral. 3x + 21 x2 + 7x + 10 - dx A) in) (x + 2)3 70.55+ (x + 2) 61 in 515
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
Tutorial Exercise Evaluate the integral using the substitution rule. sin(x) 1/3 1* dx cos(x) Step 1 of 4 To integrate using substitution, choose u to be some function in the integrand whose derivative (or some constant multiple of whose derivative) is a factor of the integrand. Rewriting a quotient as a product can help to identify u and its derivative. 70/3 1." sin(x) dx = L" (cos(x) since) dx cos?(X) Notice that do (cos(x)) = and this derivative is a...
4) Evaluate dx (4 – x²) 3/2 5) Evaluate the improper integral ſxe**dx 0 6) Express the repeating decimal 0.123 as a geometric series and then use the sum of that series to express the decimal as the ration of two integers.
25 2 6 Evaluate the integral S SS 3 cos (x2) -dx dy dz by changing the order of integration in an appropriate way. 417 o o Зу
Evaluate the integral. S (2x-1) In(18) dx (x2 – x)In 18x - +x+C 2 + x + C (21-x]ın 18x** 0 (x2 - x)In 18- x2 +x+C 0 (x2-x)in 18x - 2 + 2x +C