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3 years ago

Help me pleasei need help

Mathematics

1 answer:

DerKrebs [107]3 years ago

5 0

Answer:

1.300

Step-by-step explanation:

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Find the first four terms of this geometric sequence for a1=3 and r=-3

Natali5045456 [20]

$a_1=3;\ r=-3\\\\a_2=a_1r\to a_2=3\cdot(-3)=-9\\\\a_3=a_2r\to a_3=-9\cdot(-3)=27\\\\a_4=a_3r\to a_4=27\cdot(-3)=-81\\\\Answer:\{3;-9;\ 27;-81\}$

8 0

3 years ago

PLEASE I NEED HELP!!!

pantera1 [17]

Answer:

below

Step-by-step explanation:

f(3)=2

f(20)=0

f(8)=4

f(0)=-1

if f(x)=9 then x=4

if f(x)=4 then x=8

f(x)=0 then x=20

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4 years ago

A flag pole 20 feet tall casts a shadow 12 feet long. If John is 5 feet tall, what is the length of John's shadow while standing

posledela

His shadow will be 3 feet tall

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3 years ago

Barfoundins. The graph shows the elements what fraction of Earth's crust is Elements in Earth'scrusOther17%AluminumSo 89%OxygenS

atroni [7]

The pie chart is a percent pie chart.
Silicon is 28% of the earth crust = 28/100 = 7/25.

4 0

3 years ago