Derivatives and Integrals of Ln and e Flashcards

1

Find ∫ x/(3x²+1) dx

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

2

∫ 3x⁵ dx

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

3

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)

4

Find the derivative of y = 3x⁴

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

5

Find ∫ 3 ln e² dx

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

6

Find the derivative of y = e^x

x∙ex
ex
1/ex
ex + C

7

\int_{ }^{ }x4^{x^2}dx

\frac{4^{x^2}}{\ln16}+c→→
\frac{4^{x^2}}{\ln4}+c
4^{x^2}\ln4+c
\frac{4^{x^2}\ln4}{2}+c

8

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

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

9

Find ∫ e^{2x - 1} dx

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

10

Find the derivative of y = (ln x)³

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

11

Find ∫ 1 / (3x+2) dx

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

12

Find ∫ 2e^2x dx

e2x + C
4e2x + C
½ e2x + C
4e2x

13

Find the derivative of 4^x

ln4(4x)
4x
4x/4
4x/ln4

14

Find ∫ e^3x dx

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

15

Differentiate y = 4x³ + 5x

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

16

Find the derivative of y = ln x⁴

4/x
4/x + C
4/x · x4
1/x4 ∙ 4x3 + C

17

Differentiate y = (ln x)²

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

18

Find ∫ 1/(5x+1) dx

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

19

∫ e^{6x + 2} dx

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

20

Find the derivative of y = 8e²

undefined
16e2
0
16e

21

Find the derivative of y = x∙e^x

ex
xex + ex
(1) ∙ ex
xex + 1

22

Find the derivative of y = ln (5x²)

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

Derivatives and Integrals of Ln and e

Questions 22

Derivatives and Integrals of Ln and e

Questions 22