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4 years ago

Please help thank you

Mathematics

1 answer:

Elodia [21]4 years ago

8 0

Answer:

a1 = 6

a2 = 15

a3 = 24

a4 = 33

Step-by-step explanation:

Let k =1

a1 =-3 +9(1) = -3 +9 = 6

Let k = 2

a2 = -3 +9(2) =-3+18 = 15

Let k =3

a3 =-3 +9(3) = -3 +27 = 24

Let k = 4

a4 = -3 +9(4) =-3+36 = 33

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3 years ago

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tatiyna

Integrate indefinite integral:
$I=\int\frac{dx}{e^{2x}+3e^x+2}dx$

Solution:
1. use substitution $u=e^x$
=>
$du=e^xdx$
=>
$dx=\frac{du}{e^x}$
=>
$dx=\frac{du}{u}$
=>
$I=\int\frac{du}{u(u^2+3u+2)}du$
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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
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3. Substitute partial fractions and continue
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$=\frac{log(u)}{2}+\frac{log(u+2)}{2}-log(u+1)}$
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)

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3 years ago