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Determine the integral by making an appropriate substitution. 21) integral((2x/sqrt(x - 4)))dx

Question : Determine the integral by making an appropriate substitution. 21) integral((2x/sqrt(x - 4)))dx : 2163440

Determine the integral by making an appropriate substitution.

21) ∫((2x/√(x - 4)))dx

A) 3(x - 4)3/2 + C

B) (4/3)√(x + 4)(x - 8) + C

C) (4/3)(x - 4)3/2 + C

D) (4/3)√(x - 4)(x + 8) + C

22) ∫(tan2xsec2xdx) Use the substitution u = tanx.

A) (tan2x/2) + C

B) (sec2x/2) + C

C) (tan3x/3) + C

D) secxtanx + C

E) none of these

23) ∫(ln5x/x)dx Use the substitution u = ln5x.

A) (1/2)(ln5x)2 + C

B) (1/2)(lnx)(ln5x)2 + C

C) (5/2)(ln5x)2 + C

D) (1 - ln5x/x2) + C

E) none of these

24) ∫(ln√(x)/x)dx Use the substitution u =ln√(x).

A) 2(ln√(x))2 + C

B) ((lnx)2/4) + C

C) (1/2)(ln√(x))2 + C

D) (lnx)2 + C

E) none of these

25) ∫((cosx)8sinxdx)

A) 9(cosx)9 + C

B) (1/9)(cosx)9 + C

C) - (1/9)(cosx)9 + C

D) -9(cosx)9 + C

26) ∫(12sinx√(cosx))dx

A) -8(cosx)3/2 + C

B) 18(cosx)3/2 + C

C) 8(cosx)3/2 + C

D) -18(cosx)3/2 + C

27) ∫(x2sin(7x3 - 6)dx)

A) (1/21)cos(7x3 - 6) + C

B) - (1/21)cos(7x3 - 6) + C

C) 21cos(7x3 - 6) + C

D) -21cos(7x3 - 6) + C

28) ∫((e1/x/x2))dx

A) xe1/x + C

B) e1/x + C

C) -xe1/x + C

D) -e1/x + C

E) none of these

29) ∫((sinx/1 - cosx)dx)

A) -ln|1 - cosx| + C

B) sinxcosx + C

C) (1/2)(1 - cosx)2 + C

D) ln|1 - cosx| + C

E) none of these

30) ∫((x + (3/2)/x2 + 3x))dx

A) ln|x2+ 3x| + C

B) (1/2) ln|x2+ 3x| + C

C) (x2+ 3x)-1 + C

D) (x2+ 3x)2 + C

E) none of these

31) ∫((sec2x/(1 - 3tanx)1/2))dx

A) (1 - 3tanx)1/2 + C

B) ln|1 - 3tanx| + C

C) - (2/3)ln|1 - 3tanx| + C

D) - (2/3)(1 - 3tanx)1/2 + C

E) none of these

32) ∫(cos1/3xsinx)dx

A) cos4/3xsinx + C

B) sin2x + C

C) cos1/3x + C

D) - (3/4)cos4/3x + C

E) none of these

33) ∫((sinθcos2θ/1 + cos3θ))dθ

A) sin2θcos2θ + C

B) (1/2)(1 + cos3θ)2 + C

C) - (1/3)ln|1 + cos3θ| + C

D) (1/2)(sinθcos2θ)2 + C

E) none of these

34) ∫(√(2x2 - 3x)(3x- (9/4)))dx

A) (2x2 - 3x)1/2 + C

B) (1/2)(2x2 - 3x)3/2 + C

C) (2x2 - 3x)3/2 + C

D) (2x2 - 3x)2 + C

E) none of these

35) ∫(tan9(2xsec2(2x))dx

A) tan10x + C

B) (1/10)tan10x + C

C) 9tan8x + C

D) (1/20)tan10 x + C

E) none of these

36) ∫(x2sec2x3)dx

A) tan2x3 + C

B) (1/3)tanx3 + C

C) x2secx3 + C

D) tanx3 + C

E) none of these

37) ∫((ex/1 + 2ex)dx)

A) (1/2) ln|1 + 2ex| + C

B) e2x + C

C) ln|1 + 2ex| + C

D) (1 + 2ex)2 + C

E) none of these

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

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Enter your answer with any coefficients in front as integers or reduced fractions of form (a/b).

40) ∫((x - 1)e(3x^2 - 6x)dx)

Solution
5 (1 Ratings )

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Calculus 3 Months Ago 49 Views
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