1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Evgesh-ka [11]
3 years ago
12

Integral of 11 ln(cube root(x)) dx?

Mathematics
2 answers:
Darina [25.2K]3 years ago
5 0
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2742530

_______________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int 11\,\ell n(^3\hspace{-5}\sqrt{x})\,dx}\\\\\\ \mathsf{\displaystyle\int\!\ell n(^3\hspace{-5}\sqrt{x})\cdot 11\,dx\qquad\quad(i)}


Integration by parts:

\begin{array}{lcl}
\mathsf{u=\,\ell n(^3\hspace{-5}\sqrt{x})}&\quad\Rightarrow\quad&\mathsf{du=\dfrac{1}{^3\hspace{-5}\sqrt{x}}\cdot \dfrac{d}{dx}(^3\hspace{-5}\sqrt{x})\,dx}\\\\
&&\mathsf{du=x^{-1/3}\cdot \dfrac{1}{3}\,x^{(1/3)-1}\,dx}\\\\
&&\mathsf{du=\dfrac{1}{3}\,x^{-1/3}\cdot x^{-2/3}\,dx}\\\\
&&\mathsf{du=\dfrac{1}{3}\,x^{-1}\,dx}
\\\\\\
\mathsf{dv=11\,dx}&\quad\Leftarrow\quad&\mathsf{v=11x}
\end{array}


\mathsf{\displaystyle\int\! u\,dv=u\cdot v-\int\!v\,du}\\\\\\
\mathsf{\displaystyle\int\!\ell n(^3\hspace{-5}\sqrt{x})\cdot 11\,dx=\ell n(^3\hspace{-5}\sqrt{x})\cdot 11x-\int\!11x\cdot \frac{1}{3}\,x^{-1}\,dx}\\\\\\
\boxed{\begin{array}{c}\mathsf{\displaystyle\int\!11\,\ell n(^3\hspace{-5}\sqrt{x})\,dx=11x\,\ell n(^3\hspace{-5}\sqrt{x})-\frac{11}{3}x+C}\end{array}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)

Leno4ka [110]3 years ago
3 0
\bf \int [11\ ln\left( \sqrt[3]{x} \right)]dx\qquad 
\begin{cases}
ln\left( \sqrt[3]{x} \right)\implies ln\left( x^{\frac{1}{3}} \right)
\\ \quad \\
\frac{1}{3}ln(x)
\end{cases}\qquad thus
\\ \quad \\\\ \quad \\
\int [11\ ln\left( \sqrt[3]{x} \right)]dx\implies \int[11\cdot \frac{1}{3}ln(x)]dx\impliedby \textit{scalars to the left}
\\ \quad \\
11\cdot \frac{1}{3}\int[ln(x)]dx\implies \cfrac{11}{3}\int[ln(x)]dx

and I'm pretty sure you know what that is
You might be interested in
Please please help thank you soooo much I am sooo confused!. Plus you get 10 points
Oksi-84 [34.3K]
8 times 3 = 24 +4= 28

4+3=7 times 8 =56
5 0
3 years ago
Read 2 more answers
Please answer both thank you​
jeyben [28]

Answer:

7.

Solution given;

male=15

female=27

1st term=5*3

2nd term=3*3*3

now

Highest common factor=3

So

<u>The</u><u> </u><u>maximum</u><u> </u><u>number</u><u> </u><u>of</u><u> </u><u>groups</u><u> </u><u>that</u><u> </u><u>the</u><u> </u><u>teacher</u><u> </u><u>can</u><u> </u><u>make</u><u> </u><u>is</u><u> </u><u>3</u><u>.</u>

<u>and</u><u> </u><u>each</u><u> </u><u>team</u><u> </u><u>contains</u><u> </u><u>5</u><u> </u><u>male and</u><u> </u><u>9</u><u> </u><u>female</u><u>.</u>

7 0
3 years ago
At what point on the graph of y=2e^X -1 is the tangent line parallel to the line y= 5x -1
IgorLugansk [536]
Paralell has same slope
y=mx+b
m=slope
y=5x-1
when is the slope 5?

take the derivitive of 2e^x
f'(2e^x)=2f'(e^x)=2e^x

that is the slope
5=2e^x
divide both sides by 2
2.5=e^x
take the ln of both sides
ln2.5=x

when x=ln2.5 they are paralell
5 0
3 years ago
Need help on a systems of equations word problem
lapo4ka [179]

Answer:

brazil: 12.8 portugal: 14.769230769230769 (you need to round it)  

Step-by-step explanation:

just divide.

8 0
2 years ago
Find the equation of the line using the point-slope formula.
irina [24]

Answer:

9x-7y+28=0

Step-by-step explanation:

using formula

y-y1=m(x-x1)

y-4=9/7(x-0)

7y-28=9x

9x-7y+28=0

7 0
3 years ago
Other questions:
  • The question is.......
    8·2 answers
  • now has a book that is 3.6 meters long he cuts the Rope into two pieces one piece is 1.925 meters long how long is the other pie
    10·2 answers
  • F(×) = x^4+2×^3 determine whether the function is even or odd?
    7·1 answer
  • The Sun hits a 30 foot flagpole at a 60° angle and casts an unobstructed 52 foot shadow. If a building is built 32 feet away, wh
    11·1 answer
  • 5-2.1=? 5-2.17=? 5-2 7/8 solve make sure to re-check your self before answering or no forty points
    5·1 answer
  • Solve the equation 21p-4=12p+7/2
    14·1 answer
  • The area of the parallelogram is 315 square units. What is the height of the parallelogram?
    11·1 answer
  • A locker combination has three nonzero digits, and digits cannot be repeated. If the first digit is 3, what is the probability t
    10·1 answer
  • Minnie organizes data in a table to show the net change in the number of people subscribing and unsubscribing to her blog each m
    5·1 answer
  • PLEASE HURRY TEST
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!