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bekas [8.4K]
3 years ago
8

Question 9 of 10

Mathematics
1 answer:
Anvisha [2.4K]3 years ago
6 0

Answer:

?

Step-by-step explanation:

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Indefinite integral need help pleaseeeeeee
tatiyna
Integrate indefinite integral:
I=\int\frac{dx}{e^{2x}+3e^x+2}dx

Solution:
1. use substitution u=e^x 
=>
du=e^xdx
=>
dx=\frac{du}{e^x}
=>
dx=\frac{du}{u}
=>
I=\int\frac{du}{u(u^2+3u+2)}du
=\int\frac{du}{u(u+2)(u+1)}du
2. decompose into partial fractions
\frac{1}{u(u+2)(u+1)}
=\frac{A}{u}+\frac{B}{u+2}+\frac{C}{u+1}
where A=1/2, B=1/2, C=-1
=\frac{1}{2u}+\frac{1}{2(u+2)}-\frac{1}{u+1}
3. Substitute partial fractions and continue
I=\int\frac{du}{2u}+\int\frac{du}{2(u+2)}-\int\frac{du}{u+1}
=\frac{log(u)}{2}+\frac{log(u+2)}{2}-log(u+1)}
4. back-substitute u=e^x
=\frac{log(e^x)}{2}+\frac{log(e^x+2)}{2}-log(e^x+1)}
=\frac{x}{2}+\frac{log(e^x+2)}{2}-log(e^x+1)}

Note: log(x) stands for natural log, and NOT log10(x)

7 0
3 years ago
Expand and simplify (2x-3)(3x+4)
mojhsa [17]

Answer:

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

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

6x^2+8x-9x-12

6x^2-x-12

6 0
3 years ago
PLS HELP <br><br> (the second page is the options)
slava [35]

Answer:

D. y=2x-2

Step-by-step explanation:

The format for the equation of a line is y=mx+b, where m is the slope and b is the y-intercept of the line.

The slope of this line is 2

The y-intercept of this line is -2

Therefore, the equation for this line should look like y=2x-2

If you found this helpful, let me know by marking my answer as brainliest! Feel free to reach out with any questions. Hope this helped!

5 0
3 years ago
The length of time (T)in seconds it takes the pendulum of a clock to swing through one complete cycle is given by the formula
STatiana [176]

Answer:

T = 2 pi sqrt (L/g)

g = 32 ft/s2

here

2 = 2 (22/7) sqrt (L/32)

sqrt (L/32) = 7/22

L/32 = 49/484

L = 3.24 ft

check by hanging a weight from a 3' 3" string

Step-by-step explanation:

6 0
3 years ago
Write the slope-intercept for of the equation of a line with a slope of 5/2, and passing through (2,5)
Pani-rosa [81]
I think it would be: y=5/2x
5 0
3 years ago
Read 2 more answers
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