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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/(sinx^2)^2
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Integral of (sqrt(x)-2)^2/x
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Integral of (sin(3x))^5
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Integral of e^xsin(x/2)
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Identical expressions
- (x+ one)/(4x^ two +8x+ seven)
- (x plus 1) divide by (4x squared plus 8x plus 7)
- (x plus one) divide by (4x to the power of two plus 8x plus seven)
- (x+1)/(4x2+8x+7)
- x+1/4x2+8x+7
- (x+1)/(4x²+8x+7)
- (x+1)/(4x to the power of 2+8x+7)
- x+1/4x^2+8x+7
- (x+1) divide by (4x^2+8x+7)
- (x+1)/(4x^2+8x+7)dx
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Similar expressions
- (x-1)/(4x^2+8x+7)
- (x+1)/(4x^2+8x-7)
- (x+1)/(4x^2-8x+7)
Integral of (x+1)/(4x^2+8x+7) dx
The solution
You have entered
[src]
1 / | | x + 1 | -------------- dx | 2 | 4*x + 8*x + 7 | / 0
$$\int\limits_{0}^{1} \frac{x + 1}{\left(4 x^{2} + 8 x\right) + 7}\, dx$$
Integral((x + 1)/(4*x^2 + 8*x + 7), (x, 0, 1))
Detail solution
We have the integral:
/ | | x + 1 | -------------- dx | 2 | 4*x + 8*x + 7 | /
Rewrite the integrand
/ 4*2*x + 8 \
|--------------| /0\
| 2 | |-|
x + 1 \4*x + 8*x + 7/ \3/
-------------- = ---------------- + ---------------------------
2 8 2
4*x + 8*x + 7 / ___ ___\
|-2*\/ 3 2*\/ 3 |
|--------*x - -------| + 1
\ 3 3 / or
/ | | x + 1 | -------------- dx | 2 = | 4*x + 8*x + 7 | /
/
|
| 4*2*x + 8
| -------------- dx
| 2
| 4*x + 8*x + 7
|
/
--------------------
8 In the integral
/
|
| 4*2*x + 8
| -------------- dx
| 2
| 4*x + 8*x + 7
|
/
--------------------
8 do replacement
2 u = 4*x + 8*x
then
the integral =
/
|
| 1
| ----- du
| 7 + u
|
/ log(7 + u)
----------- = ----------
8 8 do backward replacement
/
|
| 4*2*x + 8
| -------------- dx
| 2
| 4*x + 8*x + 7
| / 2 \
/ log\7 + 4*x + 8*x/
-------------------- = -------------------
8 8 In the integral
0
do replacement
___ ___
2*\/ 3 2*x*\/ 3
v = - ------- - ---------
3 3 then
the integral =
True
do backward replacement
True
Solution is:
/ 2 \
log\7 + 4*x + 8*x/
C + -------------------
8
The answer (Indefinite)
[src]
/ | / 2 \ | x + 1 log\4*x + 8*x + 7/ | -------------- dx = C + ------------------- | 2 8 | 4*x + 8*x + 7 | /
$$\int \frac{x + 1}{\left(4 x^{2} + 8 x\right) + 7}\, dx = C + \frac{\log{\left(\left(4 x^{2} + 8 x\right) + 7 \right)}}{8}$$
The graph
The answer
[src]
log(7) log(19)
- ------ + -------
8 8
$$- \frac{\log{\left(7 \right)}}{8} + \frac{\log{\left(19 \right)}}{8}$$
=
=
log(7) log(19)
- ------ + -------
8 8
$$- \frac{\log{\left(7 \right)}}{8} + \frac{\log{\left(19 \right)}}{8}$$
-log(7)/8 + log(19)/8
The graph
Use the examples entering the upper and lower limits of integration.