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How to use it?
- Integral of d{x}:
- Integral of 1/(2x^2-5x+7)
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Integral of 9x^2-8x^3+2
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Integral of 2x^5
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Integral of x⁸
- Derivative of:
- 1/(2x^2-5x+7)
-
Identical expressions
- one /(two x^2-5x+ seven)
- 1 divide by (2x squared minus 5x plus 7)
- one divide by (two x squared minus 5x plus seven)
- 1/(2x2-5x+7)
- 1/2x2-5x+7
- 1/(2x²-5x+7)
- 1/(2x to the power of 2-5x+7)
- 1/2x^2-5x+7
- 1 divide by (2x^2-5x+7)
- 1/(2x^2-5x+7)dx
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Similar expressions
- 1/(2x^2+5x+7)
- 1/(2x^2-5x-7)
Integral of 1/(2x^2-5x+7) dx
The solution
You have entered
[src]
1 / | | 1 | -------------- dx | 2 | 2*x - 5*x + 7 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(2 x^{2} - 5 x\right) + 7}\, dx$$
Integral(1/(2*x^2 - 5*x + 7), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | -------------- dx | 2 | 2*x - 5*x + 7 | /
Rewrite the integrand
1 1
-------------- = ------------------------------------
2 / 2 \
2*x - 5*x + 7 |/ ____ ____\ |
||-4*\/ 31 5*\/ 31 | |
31/8*||---------*x + --------| + 1|
\\ 31 31 / /or
/ | | 1 | -------------- dx | 2 = | 2*x - 5*x + 7 | /
/
|
| 1
8* | ----------------------------- dx
| 2
| / ____ ____\
| |-4*\/ 31 5*\/ 31 |
| |---------*x + --------| + 1
| \ 31 31 /
|
/
-------------------------------------
31 In the integral
/
|
| 1
8* | ----------------------------- dx
| 2
| / ____ ____\
| |-4*\/ 31 5*\/ 31 |
| |---------*x + --------| + 1
| \ 31 31 /
|
/
-------------------------------------
31 do replacement
____ ____
5*\/ 31 4*x*\/ 31
v = -------- - ----------
31 31 then
the integral =
/
|
| 1
8* | ------ dv
| 2
| 1 + v
|
/ 8*atan(v)
-------------- = ---------
31 31 do backward replacement
/
|
| 1
8* | ----------------------------- dx
| 2
| / ____ ____\
| |-4*\/ 31 5*\/ 31 |
| |---------*x + --------| + 1 / ____ ____\
| \ 31 31 / ____ | 5*\/ 31 4*x*\/ 31 |
| 2*\/ 31 *atan|- -------- + ----------|
/ \ 31 31 /
------------------------------------- = --------------------------------------
31 31 Solution is:
/ ____ ____\
____ | 5*\/ 31 4*x*\/ 31 |
2*\/ 31 *atan|- -------- + ----------|
\ 31 31 /
C + --------------------------------------
31
The answer (Indefinite)
[src]
/ ____ \ / ____ |4*\/ 31 *(-5/4 + x)| | 2*\/ 31 *atan|-------------------| | 1 \ 31 / | -------------- dx = C + ---------------------------------- | 2 31 | 2*x - 5*x + 7 | /
$$\int \frac{1}{\left(2 x^{2} - 5 x\right) + 7}\, dx = C + \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{4 \sqrt{31} \left(x - \frac{5}{4}\right)}{31} \right)}}{31}$$
The graph
The answer
[src]
/ ____\ / ____\
____ |\/ 31 | ____ |5*\/ 31 |
2*\/ 31 *atan|------| 2*\/ 31 *atan|--------|
\ 31 / \ 31 /
- --------------------- + -----------------------
31 31
$$- \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{\sqrt{31}}{31} \right)}}{31} + \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{5 \sqrt{31}}{31} \right)}}{31}$$
=
=
/ ____\ / ____\
____ |\/ 31 | ____ |5*\/ 31 |
2*\/ 31 *atan|------| 2*\/ 31 *atan|--------|
\ 31 / \ 31 /
- --------------------- + -----------------------
31 31
$$- \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{\sqrt{31}}{31} \right)}}{31} + \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{5 \sqrt{31}}{31} \right)}}{31}$$
-2*sqrt(31)*atan(sqrt(31)/31)/31 + 2*sqrt(31)*atan(5*sqrt(31)/31)/31
Use the examples entering the upper and lower limits of integration.