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Evaluate the integral using integration by parts. 21) integral(x)sqrt(x + 1)dx
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# Question : Evaluate the integral using integration by parts. 21) integral(x)sqrt(x + 1)dx : 2163446

Evaluate the integral using integration by parts.

21) ∫(x)√(x + 1)dx

A) (2/3)x(x + 1)3/2 - (4/15)(x + 1)5/2 + C

B) x(x + 1)3/2 - (x + 1)5/2 + C

C) (2/3)(x + 1)3/2 - (4/15)(x + 1)5/2 + C

D) (x + 1)3/2 + (x + 1)5/2 + C

22) ∫(eaxcosbxdx)

A) eax(sinbx + cosbx) + C

B) eax(sinbx - cosbx) + C

C) eax((bsinbx + acosbx/a2 + b2)) + C

D) (1/2b)eaxcos2bx + C

23) ∫(eaxsinbxdx)

A) (1/2b)eaxcos2bx + C

B) eax(sinbx + cosbx) + C

C) eax((asinbx - bcosbx/a2 + b2)) + C

D) eax(sinbx - cosbx) + C

24) ∫(e2xsin3xdx)

A) - e2x(sin3x - 3cos3x) + C

B) (1/13)e2x(sin3x - 3cos3x) + C

C) (1/13)e2x(2sin3x - 3cos3x) + C

D) e2x(sin3x - cos3x) + C

25) ∫(sec4xdx)

A) (1/5)sec5xtanx + C

B) 4sec3xtanx+ C

C) (1/3)sec2xtanx + (2/3)tanx + C

D) sec2xtanx + tanx + C

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

26) Does this integral ∫(2xexdx) = 2ex(x - 1) + C?

Enter "yes" or "no".

27) Does this integral ∫(t3cost dt) = (t3 - 6t)sint + 3(t2 - 2)cost + C?

Enter "yes" or "no".

28) Does this integral ∫((ln(2x)/x2)dx) = - (1 + ln2 + lnx/x) + C?

Enter "yes" or "no".

29) Does this integral ∫(3x√(4x + 3)dx) = (3(2x - 1)(4x + 3)3/2/20) + C?

Enter "yes" or "no".

30) Does this integral ∫(x2sin2xdx) = ((1 - 2x2)cos2x/4) + (xsin2x/2) + C?

Enter "yes" or "no".

31) Does this integral ∫(xexsinxdx) = (-ex((x - 1)cosx +xsinx)/2) + C?

Enter "yes" or "no".

32) Does this integral ∫(xsin10xdx) = (1/100)sin10x - (x/10)cos10x + C?

Enter "yes" or "no".

33) Does this integral ∫(xcos5xdx) = (1/5)xsin5x - (1/25) cos5x + C?

Enter "yes" or "no".

34) Does this integral ∫(x3lnxdx) = (1/4)x4lnx + (1/16)x4 + C?

Enter "yes" or "no".

35) Does this integral ∫(xe-3xdx) = - (1/3)xe-3x - (1/9)e-3x + C?

Enter "yes" or "no".

36) Does this integral ∫(xsec2xdx) = xtanx + ln|cosx| + C?

Enter "yes" or "no".

37) Does this integral ∫(cosx/(3sinx + 1)2)dx = (1/3(3sinx + 1)) + C?

Enter "yes" or "no".

38) Does this integral ∫(x2exdx) = x2ex - 2(xex - ex) + C?

Enter "yes" or "no".

## Solution 5 (1 Ratings )

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Calculus 3 Months Ago 52 Views