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MakcuM [25]
3 years ago
12

Please help me I will make you the brainiest

Mathematics
2 answers:
Anna35 [415]3 years ago
5 0
Answer:...


Explanation:
Sedaia [141]3 years ago
4 0
Em that’s abit hard
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What is the antiderivative of 3x/((x-1)^2)
Maslowich

Answer:

\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C

Step-by-step explanation:

Given

\int \:\:3\cdot \frac{x}{\left(x-1\right)^2}dx

\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx

=3\cdot \int \frac{x}{\left(x-1\right)^2}dx

\mathrm{Apply\:u-substitution:}\:u=x-1

=3\cdot \int \frac{u+1}{u^2}du

\mathrm{Expand}\:\frac{u+1}{u^2}:\quad \frac{1}{u}+\frac{1}{u^2}

=3\cdot \int \frac{1}{u}+\frac{1}{u^2}du

\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx

=3\left(\int \frac{1}{u}du+\int \frac{1}{u^2}du\right)

as

\int \frac{1}{u}du=\ln \left|u\right|     ∵ \mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)

\int \frac{1}{u^2}du=-\frac{1}{u}        ∵     \mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1

so

=3\left(\ln \left|u\right|-\frac{1}{u}\right)

\mathrm{Substitute\:back}\:u=x-1

=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)

\mathrm{Add\:a\:constant\:to\:the\:solution}

=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C

Therefore,

\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C

4 0
3 years ago
last month a parking lot had 22 spaces in each of its rows recently the lot expanded and 4 spaces were added to each row if the
Vika [28.1K]
368 spaces now, why?
There are 22 spaces per row, and we know there are 8 rows, so thats 176 spaces last month,
we add 4 spaces to each row of 22, thats 26 spaces per row, 26 * 8 = 368 total spaces
7 0
3 years ago
Sales tax is calculated as a percentage of the sales price. If sales tax is 7%, what is the sales tax on clothing that costs $15
dalvyx [7]
10.50 and the total cost will be 160.50.
8 0
3 years ago
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Y=2(x-1)^2+1 in standard form
Ronch [10]

Answer:

2(x^2+1-2x)+1=

2x2+2-4x+1=

2x2-4x+3

Step-by-step explanation:

7 0
3 years ago
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PLEASE HELP RUNNING OUT OF TIME .!!! A boat designer plans to construct a triangular sail with base 90 centimeters and altitude
Korolek [52]

Answer:

b

Step-by-step explanation:

4 0
3 years ago
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