Question

Determine the following indefinite integral...

Answer 1

\[\int\limits_{}^{} 3x^\frac{ 2 }{ 3 } + 4x ^{-\frac{ 1 }{ 3 }} + 7 dx \]

Answer 2

Use this:
\[\int x^ndx = \frac{1}{n+1}x^{n+1} + C\]

Answer 3

my answer was \[\frac{ 9 }{ 5 }x ^{\frac{ 5 }{ 3 }} + 6x + C\]
but i got it wrong

Answer 4

i know how to solve the problem and i checked with differentiation .. and it seems right so i dont understand what i did wrong

Answer 5

?

Answer 6

You will have 4 terms.
1) Integrate \[\int 3x^{\frac{2}{3}}dx\]
2) Integrate \[\int4x^{-\frac{1}{3}}dx\]
3) Integrate \[\int 7 dx\]

Then add the the results you get from 1, 2, and 3.

Answer 7

Here is what you got when you differentiate your answer:
\[\frac{d}{dx}(\frac{ 9 }{ 5 }x ^{\frac{ 5 }{ 3 }} + 6x + C)\]\[=\frac{ 9 }{ 5 }\times\frac{5}{3}x ^{\frac{ 2 }{ 3 }} + 6\]\[=3x ^{\frac{ 2 }{ 3 }} + 6\]
The constant term is not right. One term is missing.

Answer 8

@callisto sorry im a little slow lol
why is it that we have to multiply (9/5) by (5/3) and why 6 is left like that.. if you can..
cus i thought
6x^(2/3) was seperate or whatever and \[7 \int\limits_{}^{} dx\] was a constant

Answer 9

oh wait you're showing me the differentiation of my answer lol nevermind @callisto

Answer 10

To show that after differentiating your answer, you cannot get back the polynomial in the question, which implies you did it wrong....

Answer 11

\[\int 7 dx = 7 \int (1) dx = 7\int x^{0} dx\]How, you can use that power rule again to integrate it :)

Answer 12

so is it \[ \frac{ 9 }{ 5 }x^{\frac{ 5 }{ 3 }} + 6x ^{\frac{ 2 }{ 3 }} + \frac{ 7 }{ 2 } + C\] ? @Callisto

Answer 13

No... Check the third term...

Answer 14

\[\int 7dx =?\]

Answer 15

\[\int 7 dx = 7 \int (1) dx = 7\int x^{0} dx\]Using the following to integrate:
\[\int x^ndx = \frac{1}{n+1}x^{n+1} + C\]
n=...?

Answer 16

sorry for all the trouble my brain just loves fighting with me -,- lol XD

Answer 17

No...
\[\int x^n dx = \frac{1}{n+1}x^{n+1}+C\]
Integrate\[\int x^0dx\]Sub n=0 into the formula. What do you get on the right side?

Answer 18

1

Answer 19

No

Answer 20

Sub n=0
\[\frac{1}{n+1}x^{n+1}+C = \frac{1}{0+1}x^{0+1}+C = ...?\]

Answer 21

DePaz: Please note that x^0 is equal to 1.

Thus, the integral of x^0 dx simplifies to Int(dx). Or you could look at it as Int(1dx). Can you evaluate that, given the power rule for integration given by Callisto above? Let me retype that here: Int(x^n) = [x^(n+1)]/(n+1) + C.

Answer 22

i put it as 1 and i got it right.
so i got it right.. idk why @ castillo said no..
i put \[\frac{ 9 }{ 5 }x^{\frac{ 5 }{ 3 }} + 6x ^{\frac{ 2 }{ 3 }} + 7x + C\]