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How to use it?
- Integral of d{x}:
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Integral of (7x-3)
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Integral of 3*dx/(x^2+16)
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Integral of 2xe^xdx
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Integral of (2x+1)*e^(-2x)
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Identical expressions
- three *dx/(x^ two + sixteen)
- 3 multiply by dx divide by (x squared plus 16)
- three multiply by dx divide by (x to the power of two plus sixteen)
- 3*dx/(x2+16)
- 3*dx/x2+16
- 3*dx/(x²+16)
- 3*dx/(x to the power of 2+16)
- 3dx/(x^2+16)
- 3dx/(x2+16)
- 3dx/x2+16
- 3dx/x^2+16
- 3*dx divide by (x^2+16)
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Similar expressions
- 3*dx/(x^2-16)
Integral of 3*dx/(x^2+16) dx
The solution
You have entered
[src]
1 / | | 3 | ------- dx | 2 | x + 16 | / 0
$$\int\limits_{0}^{1} \frac{3}{x^{2} + 16}\, dx$$
Integral(3/(x^2 + 16), (x, 0, 1))
Detail solution
We have the integral:
/ | | 3 | ------- dx | 2 | x + 16 | /
Rewrite the integrand
/3 \
|--|
3 \16/
------- = ----------
2 2
x + 16 /-x \
|---| + 1
\ 4 / or
/ | | 3 | ------- dx | 2 = | x + 16 | /
/
|
| 1
3* | ---------- dx
| 2
| /-x \
| |---| + 1
| \ 4 /
|
/
------------------
16 In the integral
/
|
| 1
3* | ---------- dx
| 2
| /-x \
| |---| + 1
| \ 4 /
|
/
------------------
16 do replacement
-x
v = ---
4 then
the integral =
/
|
| 1
3* | ------ dv
| 2
| 1 + v
|
/ 3*atan(v)
-------------- = ---------
16 16 do backward replacement
/
|
| 1
3* | ---------- dx
| 2
| /-x \
| |---| + 1
| \ 4 / /x\
| 3*atan|-|
/ \4/
------------------ = ---------
16 4 Solution is:
/x\
3*atan|-|
\4/
C + ---------
4
The answer (Indefinite)
[src]
/ /x\ | 3*atan|-| | 3 \4/ | ------- dx = C + --------- | 2 4 | x + 16 | /
$$\int \frac{3}{x^{2} + 16}\, dx = C + \frac{3 \operatorname{atan}{\left(\frac{x}{4} \right)}}{4}$$
The graph
The answer
[src]
3*atan(1/4)
-----------
4
$$\frac{3 \operatorname{atan}{\left(\frac{1}{4} \right)}}{4}$$
=
=
3*atan(1/4)
-----------
4
$$\frac{3 \operatorname{atan}{\left(\frac{1}{4} \right)}}{4}$$
3*atan(1/4)/4
The graph
Use the examples entering the upper and lower limits of integration.