3 years ago

Will give Brainliest! if right!

1 answer:

8 0

The mode is "C. 1 & 31".
That is correct because mode is the number that appear most often in a number set, and as 2 numbers so happened to both appear twice they are both the mode.

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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

1/5 ÷ 2. simple for a couple of points lol

Sergio039 [100]

0.1

Have a amazing day!!

8 0

3 years ago

Read 2 more answers

If x>0, what values of c and d make the equations true?

pantera1 [17]

Answer: