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
deff fn [24]
3 years ago
8

Integrate x+1/sqrt(x). I know that the answer is 2/3 • sqrt(x) • (x+3) + C, but I don't know how it is simplified from 2/3 • x^3

/2 + 2 • x^1/2 + C. Please explain this step in detail? Thank you!

Mathematics
1 answer:
Andreas93 [3]3 years ago
3 0

\displaystyle\int\frac{x+1}{\sqrt x}\,\mathrm dx=\int\frac x{x^{1/2}}+\frac1{x^{1/2}}\,\mathrm dx

=\displaystyle\int x^{1/2}+x^{-1/2}\,\mathrm dx

By the power rule,

=\dfrac{x^{3/2}}{\frac32}+\dfrac{x^{1/2}}{\frac12}+C

(this seems to be the step you're not getting?)

=\dfrac23x^{3/2}+2x^{1/2}+C

The next step is to pull out a common factor of x^{1/2} from the antiderivative:

x^{3/2}=x^{1/2+1}=x^{1/2}\cdot x^1

so that the final result is

\dfrac23x^{3/2}+2x^{1/2}+C=\dfrac23x^{1/2}(x+3)+C

You might be interested in
Point A was marked on a number line at -3. Then point A is then moved to a position, point B, that is 11 less than its starting
ira [324]

Answer:  -6

Step-by-step explanation:

i took the test my guy

7 0
3 years ago
...............................
enyata [817]

Answer:

addition prop of equality

Step-by-step explanation:

youre welcome

4 0
3 years ago
A Cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddies c
NemiM [27]
1.75 + 0.25x ≤ 15
where x is equal the number of miles.

The key to solving an inequality is just temporarily making the ≤ symbol a =. Then solve for x like any other algebraic equation. Once you find the value of x, you will have solved the inequality. Make sure to add back the ≤ when you are done. 

15 - 1.75 = 13.25
13.25/0.25 = x 
x = 53
add back the ≤
x ≤ 53
This means Eddies can travel up to 53 miles with his $15.
4 0
3 years ago
the pool at the apartment is 30 feet long 20 feet wide and five feet deep it has been filled to 4 feet how many more cubic inche
pickupchik [31]

Answer:

600 cubic feet

Step-by-step explanation:

6 0
3 years ago
Given f(x) = 2^x and g(x)=x+1, (fog)(x)=​
mixas84 [53]

Answer:

(f ○ g)(x) = 2^{x+1}

Step-by-step explanation:

Substitute x = g(x) into f(x) , that is

(f ○ g)(x)

= f(g(x))

= f(x + 1)

= 2^{x+1}

3 0
3 years ago
Read 2 more answers
Other questions:
  • A hiker at the top of a mountain spots his car back in the parking lot at the
    8·1 answer
  • Shelbi wants to run one lap around the track as fast as her friend Annabelle, who can run one lap in 1 minute and 10 seconds. Sh
    8·2 answers
  • The altitude in feet of a plan minutes after is given by =3400 +600. How many after liftoff is the plane at an altitude of 21,00
    11·1 answer
  • Suppose that F′(x)=f(x) and G′(x)=g(x). Which statements are true? A. If F and G differ by a constant, then f=g. B. If f and g d
    8·1 answer
  • F the graph of y=ax+b/x+c has a horizontal asymptote y=2 and a vertical asymptote x=-3 then a+c=?
    14·1 answer
  • 1.) Given that the diameter of the circle is 36 inches, find the radius and the circumference. Leave your answer in terms of . S
    11·1 answer
  • A bag contains 4 orange tiles, 6 red tiles, and 8 black tiles. You select one tile at random from the bag. What is the probabili
    7·2 answers
  • Use the scientific calculator if needed<br> Sin^-1 squareroot 2/2
    10·1 answer
  • PLZ HURRY IT'S URGENT!!!
    6·1 answer
  • Translate the phrase into a variable expression. Use the letter p to name the
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!