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3 years ago

Multiply the following and simplify.

Mathematics

1 answer:

Yuki888 [10]3 years ago

5 0

What are we multiplying exactly?

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Calculus 2 Master needed, show steps with partial fraction decomposition <img src="https://tex.z-dn.net/?f=%5Cint%283x%5E2-26x%2

Vladimir79 [104]

Answer:

-ln|x−5| + 2 ln(x²+4) + 3 tan⁻¹(x/2) + C

Step-by-step explanation:

The fraction will be split into a sum of two other fractions.

The first fraction will have a denominator of x − 5. The numerator will the a polynomial of one less order, in this case, a constant A.

The second fraction will have a denominator of x² + 4. The numerator will be Bx + C.

$\frac{3x^{2}-26x+26}{(x-5)(x^{2}+4)}=\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}$

Combine the two fractions back into one using the common denominator.

$\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}=\frac{A(x^{2}+4)+(Bx+C)(x-5)}{(x-5)(x^{2}+4)}$

This numerator will equal the original numerator.

$A(x^{2}+4)+(Bx+C)(x-5)=3x^{2}-26x+26\\Ax^{2}+4A+Bx^{2}-5Bx+Cx-5C=3x^{2}-26x+26\\(A+B)x^{2}+(C-5B)x+(4A-5C)=3x^{2}-26x+26$

Match the coefficients.

$A+B=3\\C-5B=-26\\4A-5C=26$

Solve the system of equations.

$A=-1\\B=4\\C=-6$

So we can rewrite the integral as:

$\int {(\frac{-1}{x-5}+\frac{4x-6}{x^{2}+4}) } \, dx$

Solving:

$\int {\frac{-1}{x-5}\, dx + \int {\frac{4x}{x^{2}+4}} \, dx - \int {\frac{6}{x^{2}+4} } \, dx$

$-\int {\frac{1}{x-5}\, dx + 2\int {\frac{2x}{x^{2}+4}} \, dx - 6\int {\frac{1}{x^{2}+4} } \, dx$

$-ln|x-5| + 2ln(x^{2}+4) - 6(\frac{1}{2} tan^{-1}(\frac{x}{2} )) + C$

$-ln|x-5| + 2ln(x^{2}+4) - 3 tan^{-1}(\frac{x}{2} ) + C$

5 0

3 years ago

Which problem can be solved by finding 24 ÷ 8?

Tems11 [23]

$24 \div 8 = 3$

5 0

4 years ago

Solve and show working for 1/2÷8

JulsSmile [24]

0.0625. 1÷2=0.5÷8=0.0625

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3 years ago

Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (15 cents)/(1 kilowa

shutvik [7]

So electricity costs 15cents every 1,000 watts used, and if he watches tv for 2hrs every day for a month that’s 60 hours (2*30) And every hour he watches tv it’s 150 watts. They want you to do the 60 hrs times 150watts which is 9,000 (amount of watts he uses in the month) and remember 1,000 watts is 15cents

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3 years ago

Juan needs to take an Uber to get to the movies. The Uber charges $1.50 for the first mile, and then $1.55 for each mile after t

nordsb [41]

Answer: 5.8 miles

Step-by-step explanation:

10.49 - 1.5 = 8.99

8.99 / 1.55 = 8.99

7 0

3 years ago