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
uranmaximum [27]
3 years ago
14

\int (x+1)\sqrt(2x-1)dx

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
6 0

Answer:

\int (x+ 1) \sqrt{2x-1} dx =  \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C

Step-by-step explanation:

\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v =  \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}

\int (x+1)\sqrt(2x-1)dx\\\\   = uv - \int v du                              

= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  [ \ u = x + 1 => du = dx  \ ]    

= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\=  \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\

You might be interested in
12. Write the equations in point-slope form of the line that passes through
mario62 [17]

Answer: Y-1=-1/8(X-3)

Step-by-step explanation:

Point slope form is Y-y1=m(x-x1)

the slope here is 2-1/-5-3 = 1-/8

so its Y-1=-1/8(X-3)

6 0
3 years ago
Read 2 more answers
PLEASE CHOSE THE RIGHT ANSWER AND EXPLAIN WHY YOU CHOSE IT PLEASE
Nikitich [7]

Answer:

D

Step-by-step explanation:

See attached image.

7 0
2 years ago
The vertices of the trapezoid are the origin along with A(4p,4q), B(4r,4q), and C(4s,0). Find the midpoint of the midsegment of
Nesterboy [21]

Check this attachment

8 0
3 years ago
Which statement is true?
valentinak56 [21]

Answer:

  |-3| = 3 and -|-4| = -4

Step-by-step explanation:

The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.

|-3| = 3 (true) and -|-4| = -4 (true)   ⇒ this statement is true

|-3| = 3 (true) and |-4| = -4 (false)   ⇒ this statement is false

-|3| = 3 (false) and |4| = 4 (true)   ⇒ this statement is false

|-3| = 3 (true) and -|4| = 4 (false)   ⇒ this statement is false

__

<em>Additional comment</em>

A compound "and" statement is only true if <u>all</u> of the parts of it are true.

8 0
1 year ago
HELP ME PLS
Alisiya [41]

Answer:

7/24

Step-by-step explanation:

you have to have a common denominator so you multiply one denominator to the opposite numerator and denominator and vice versa. So for 2/3 you should get 16/24 and for 3/8 you should get 9/24. Then you subtract 9 from 16 and get 7. So the answer is 7/24

3 0
2 years ago
Read 2 more answers
Other questions:
  • Some students prepare 3 diffrerent snacks. They make 1/8 pound bags of nut mix, 1/4 pound bags of cherries, and 1/6 pound bags o
    6·1 answer
  • Also can u help on all these
    13·1 answer
  • Help i need answers for these problems pls
    14·1 answer
  • Name another name for slope.<br> I’ll mark you brainlyist
    9·1 answer
  • Evaluate the expression, 12w - 5 if w = 4*<br> (2 Points)<br> Enter your answer
    12·1 answer
  • Find the volume of the cylinder.<br><br> r = 5 cm<br><br> h = 9 cm
    13·1 answer
  • What is the sq root of 66666647362617?
    7·2 answers
  • Plssssss help giving brainly
    6·2 answers
  • PMark for Review
    12·1 answer
  • In a bar graph, a 12 cm bar represents 96 kg. What will be the weight represented by a 5 cm bar? (A) 5 kg (B) 13 kg (C) 40 kg (D
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!