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
anyanavicka [17]
3 years ago
12

Help with this integral

="TexFormula1" title=" \int\limits \frac{dx}{x^{2}-4x-13}" alt=" \int\limits \frac{dx}{x^{2}-4x-13}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
charle [14.2K]3 years ago
6 0
x^2-4x-13=(x-2)^2-17

x-2=\sqrt{17}\sec y
\mathrm dx=\sqrt{17}\sec y\tan y\,\mathrm dy

\displaystyle\int\frac{\mathrm dx}{x^2-4x-13}=\int\frac{\sqrt{17}\sec y\tan y}{(\sqrt{17}\sec y)^2-17}\,\mathrm dy
=\displaystyle\frac1{\sqrt{17}}\int\frac{\sec y\tan y}{\sec^2y-1}\,\mathrm dy
=\displaystyle\frac1{\sqrt{17}}\int\frac{\sec y\tan y}{\tan^2y}\,\mathrm dy
=\displaystyle\frac1{\sqrt{17}}\int\frac{\sec y}{\tan y}\,\mathrm dy
=\displaystyle\frac1{\sqrt{17}}\int\frac{\frac1{\cos y}}{\frac{\sin y}{\cos y}}\,\mathrm dy
=\displaystyle\frac1{\sqrt{17}}\int\csc y\,\mathrm dy
=-\dfrac1{\sqrt{17}}\ln|\csc y+\cot y|+C

\sec y=\dfrac{x-2}{\sqrt{17}}\iff y=\sec^{-1}\dfrac{x-2}{\sqrt{17}}
\implies\csc y=\dfrac{x-2}{\sqrt{(x-2)^2-17}}=\dfrac{x-2}{\sqrt{x^2-4x-13}}
\implies\cot y=\dfrac{\sqrt{17}}{\sqrt{(x-2)^2-17}}=\dfrac{\sqrt{17}}{\sqrt{x^2-4x-13}}

\displaystyle\int\frac{\mathrm dx}{x^2-4x-13}=-\dfrac1{\sqrt{17}}\ln\left|\frac{x-2+\sqrt{17}}{\sqrt{x^2-4x-13}}\right|+C
You might be interested in
HELP WITH THESE TWO MATH QUESTIONS PLEASE!!!<br> ASAP!
Brilliant_brown [7]
The first picture would be choice answer c because the number of x's represent how many birds wings are this size. The number on the tic mark represents the size of the wing span. So you would take the number of x's times the tic mark represented under it. There are 3 birds with 3 1/8  wingspan so it wold be 3 1/8 *3. Hoped this helps for the first one!
8 0
3 years ago
How do you find measures using postulates and theorems?
Dennis_Churaev [7]
Just use the definitions and put them in order to explain the problem.m. for instance. why are angles a and b vertical angles? they are adjacent and they are supplementary.
8 0
3 years ago
Answer ASAP: What is the set of the four consecutive integers, the largest of which is -234?
Elza [17]
I’m pretty sure the answer is -237, -236, -235, and -234. Because -234 would be the greatest of that consecutive set.
5 0
3 years ago
A water pipe under Buckingham Palace is 59 m long. A water pipe under the White House is 36 m long. What is the difference in th
RUDIKE [14]
59m - 36m = 23m 

23m is your answer.
7 0
3 years ago
Read 2 more answers
Anyone want to talk? whats 95x4?
grin007 [14]

Answer:

95*4=380

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Given that abc is congruent to def, ac=21x-19 and df=3x+17 solve for x
    14·1 answer
  • Mrs .Nelson has a rectangular flower box that is 5 feet long and 2 feet tall. she wants the width of the box to be more than 5 f
    11·1 answer
  • Kaitlin's recipe says to bake a pie at 425°F. To the nearest whole degree, what temperature Celsius should she bake the pie?
    12·1 answer
  • Someone please help with A, B and C?
    14·2 answers
  • Answer pleaseeeeeeeeee
    11·1 answer
  • 6 people go to restaurant they arrived randomly at different times in how many ways can they arrive
    5·2 answers
  • In AABC, AB = CA and mZA = 110°. Find mZC.
    8·1 answer
  • What is the value of x?
    8·1 answer
  • Determine whether y varies directly with x, if so find the constant of variation
    9·1 answer
  • Please answer 1 and 2<br> Will mark brainliest!!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!