Derivatives and Integrals Involving Logarithms and Exponentials Flashcards

1

Find ∫ x/(3x²+1) dx

1/6 |3x2+1| + C
(6x)/(3x2+1)
1/6 ln |3x2+1| + C
6 ln |3x2+1| + C

2

Using log rules, which expression is equivalent to ln(x²y³z)

2ln x + 3ln y + ln z
1/x + 1/y + 1/z
2ln x + 3ln y + 4ln z
6(ln x + ln y + ln z)

3

Find the derivative of y = e^x

x∙ex
ex
1/ex
ex + C

4

Find the derivative of y = (ln x)³

3(ln x)2
3/x
3(ln x) 1/x
3(ln x)2∙ 1/x

5

Find the derivative of y = x∙e^x

xex + 1
xex + ex
(1) ∙ ex
ex

6

Find ∫ e^{2x - 1} dx

(2x-1)e2x-2
½ e2x-1
½ ex + C
½ e2x-1 + C

7

∫ 3x⁵ dx

x5/2 + C
x6/6 + C
x6/2
x6/2 + C

8

Find the derivative of y = 8e²

16e
undefined
0
16e2

9

Differentiate y = (ln x)²

(ln x) / x
2 ln x
2/x
(2 ln x) / x

10

Find ∫ 1/(5x+1) dx

1/5 | ln (5x+1) | +C
1/5 ln | (5x+1) | +C
5/(5x + 1)
1/5 (5x+1) + C

11

Find ∫ 1 / (3x+2) dx

(ln |3x+2|)/3 + C
(ln |3x+2|)/3
(ln |u|)/3 + C
(ln |3x+2|) + C

12

Find the derivative of y = ln (5x²)

10x
2/x2
2/x
1/(5x2)

13

Find ∫ 2e^2x dx

½ e2x + C
e2x + C
4e2x
4e2x + C

14

Find the derivative of y = ln x⁴

4/x · x4
4/x
1/x4 ∙ 4x3 + C
4/x + C

15

Differentiate y = 4x³ + 5x

12x2 + 5
12x2 + 5 + C
x/4 + 5x2 + C
x/4 + 5x2

16

Find the area under y = 1/x from x = 3 to x = 9

ln 3 sq units
e9 - e3 sq units
ln 3 - ln 9 sq units
- 2/9 sq units

17

Find ∫ e^3x dx

1/3 e3x + C
3e3x + C
1/3 ex + C
1/3 ln |3x| +C

18

∫ e^{6x + 2} dx

1/6 e6x + 2 + C
1/2 e6x + 2 + C
6e6x + 2 + C
1/6 e6x + 2

19

Find the derivative of y = 3x⁴

12x3
x5/5 + C
x5/5
4x3/3

20

Find ∫ 3 ln e² dx

6x + C
6 ln e + C
3x + C
3 / (ln e2) + C

Derivatives and Integrals Involving Logarithms and Exponentials

Questions 20

Derivatives and Integrals Involving Logarithms and Exponentials

Questions 20