Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of x^2*e^(x*(-2))
-
Integral of e^(-x^3)
-
Integral of -exp(-3*x)
- Integral of (xcosx)/(2+3x^3)
-
Identical expressions
- eight /(x*x+ four)
- 8 divide by (x multiply by x plus 4)
- eight divide by (x multiply by x plus four)
- 8/(xx+4)
- 8/xx+4
- 8 divide by (x*x+4)
- 8/(x*x+4)dx
-
Similar expressions
- (2*x^3-40*x-8)/(x*(x+4)*(x-2))
- 8/(x*x-4)
- 2x^3-40x-8/x(x+4)(x-2)
Integral of 8/(x*x+4) dx
The solution
You have entered
[src]
2 / | | 8 | ------- dx | x*x + 4 | / 0
$$\int\limits_{0}^{2} \frac{8}{x x + 4}\, dx$$
Integral(8/(x*x + 4), (x, 0, 2))
Detail solution
We have the integral:
/ | | 8 | ------- dx | x*x + 4 | /
Rewrite the integrand
/8\
|-|
8 \4/
------- = ----------
x*x + 4 2
/-x \
|---| + 1
\ 2 / or
/ | | 8 | ------- dx = | x*x + 4 | /
/ | | 1 2* | ---------- dx | 2 | /-x \ | |---| + 1 | \ 2 / | /
In the integral
/ | | 1 2* | ---------- dx | 2 | /-x \ | |---| + 1 | \ 2 / | /
do replacement
-x
v = ---
2 then
the integral =
/ | | 1 2* | ------ dv = 2*atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 /x\ 2* | ---------- dx = 4*atan|-| | 2 \2/ | /-x \ | |---| + 1 | \ 2 / | /
Solution is:
/x\
C + 4*atan|-|
\2/
The answer (Indefinite)
[src]
/ | | 8 /x\ | ------- dx = C + 4*atan|-| | x*x + 4 \2/ | /
$$\int \frac{8}{x x + 4}\, dx = C + 4 \operatorname{atan}{\left(\frac{x}{2} \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.