Question : Determine the integral by making an appropriate substitution. 1) integral((x^7 - 2x^6)5(7x^6 - 12x^5))dx : 2163437

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine the integral by making an appropriate substitution.

1) ∫((x⁷ - 2x⁶)⁵(7x⁶ - 12x⁵))dx

A) (1/5)(x⁷ - 2x⁶)⁵ + C

B) (1/6)(x⁷ - 2x⁶)⁶ + C

C) 7x⁶ - 12x⁵ + C

D) (x⁷ - 2x⁶)⁶ + C

2) ∫((6x⁵dx/(4 + x⁶)³))

A) (1/4)(4 + x⁶)⁴ + C

B) - (6x⁵/(4 + x⁶)²) + C

C) - (1/4(4 + x⁶)⁴) + C

D) - (1/2(4 + x⁶)²) + C

3) ∫(x³)√(x⁴ + 9)dx

A) (2/3)(x⁴ + 9)^3/2 + C

B) - (1/2)(x⁴ + 9)^-1/2 + C

C) (8/3)(x⁴ + 9)^3/2 + C

D) (1/6)(x⁴ + 9)^3/2 + C

4) ∫(10x²)(4)√(7 + 3x³)dx

A) 8(7 + 3x³)^5/4 + C

B) - (20/3)(7 + 3x³)^-3/4 + C

C) 10(7 + 3x³)^5/4 + C

D) (8/9)(7 + 3x³)^5/4 + C

5) ∫(x³√(x⁴ + 7)dx)

A) (1/6)x⁴(x⁴ + 7)^3/2 + C

B) (2/3)(x⁴ + 7)^3/2 + C

C) (1/6)(x⁴ + 7)^3/2 + C

D) (1/8√(x⁴ + 7)) + C

6) ∫((t²/(5)√(8 + t³)) dt)

A) (1/12(8 + t³)⁴) + C

B) (5/18)(8 + t³)^4/5 + C

C) (5/12)(8 + t³)^4/5 + C

D) (5/12)t³(8 + t³)^4/5 + C

7) ∫(4e^5x)dx

A) 4e^5x + C

B) (4/5)e^5x + C

C) (1/5)e^5x + C

D) (4e^5x+1/5x + 1) + C

8) ∫((x⁵/e^{x^6})dx)

A) - (1/6e^{x^6-1}) + C

B) - (1/6e^{x^6}) + C

C) (5x⁴/e^{x^6}) + C

D) (1/e^{x^6}) + C

9) ∫((e^{1/t^6}/t⁷) dt)

A) - (e^{1/t^6}/6t⁶) + C

B) - e^{1/t^6} + C

C) - (e^{1/t^6}/6) + C

D) (e^{-1/t^6}/6) + C

10) ∫(((lnx)⁹/x))dx

A) (lnx)¹⁰ + C

B) ((lnx)⁸/8) + C

C) ((lnx)¹⁰/10x) + C

D) ((lnx)¹⁰/10) + C

11) ∫((sin⁵xcosxdx))

A) (sin⁵x/5) + C

B) (sin⁶x/5) + C

C) (sin⁶x/6) + C

D) (sin⁵x/6) + C

12) ∫(sinxcos⁷x)dx

A) (1/8)sin⁸x + C

B) - (1/8)cos⁸x + C

C) 7sin⁷x + C

D) -7cos⁷x + C

13) ∫(-9x³sinx⁴dx)

A) 36cosx⁴ + C

B) (9/4)cosx⁴ + C

C) 9cosx⁴ + C

D) (9/4)x⁴cosx⁴ + C

14) ∫((16x(3)√(8x² - 17)))dx

A) ((8x² - 17)^4/3/3) + C

B) ((8x² + 17)⁴/32) + C

C) (3(8x² + 17)^4/3/4) + C

D) (3(8x² - 17)^4/3/4) + C

15) ∫((18x² - 5/(6x³ - 5x)²))dx

A) ((6x³ - 5x)²/2) + C

B) - (1/6x³ - 5x) + C

C) (1/6x³ - 5x) + C

D) ((6x³ - 5x)³/3) + C

16) ∫(4(2x + 5)³dx)

A) (3/8)(2x + 5)⁴ + C

B) (1/4)(2x + 5)⁴ + C

C) (1/2)(2x + 5)⁴ + C

D) (3/4)(2x + 5)⁴ + C

17) ∫(3(2x + 5)³dx)

A) (1/4)(2x + 5)⁴ + C

B) (3/4)(2x + 5)⁴ + C

C) (3/8)(2x + 5)⁴ + C

D) (1/2)(2x + 5)⁴ + C

18) ∫((1/3√(x))((5)√6 + √(x)))dx

A) (5(6 + √(x))^6/5/9) + C

B) (5(6 + √(x))^6/5/6) + C

C) (5(6 + √(x))^6/5/18) + C

D) ((6 + √(x))⁶/9) + C

19) ∫((x/(7x² + 3)⁵))dx

A) - (7/3(7x² + 3)⁶) + C

B) - (7/3(7x² + 3)⁴) + C

C) - (1/14(7x² + 3)⁶) + C

D) - (1/56(7x² + 3)⁴) + C

20) ∫((x - 1)⁷dx)

A) (1/8)(x - 1)⁸ + C

B) (1/2) x² + (1/8)(x - 1)⁸ + C

C) (1/9)(x - 1)⁹ + (1/8)(x - 1)⁸ + C

D) (1/16(x - 1)⁸) + C