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+1)/(x^2+2x-1)
- Integral of ln|secx+tanx|dx
-
Integral of dx/(5*x^2+3)
-
Integral of dx/(4x+3)^5
-
Identical expressions
- dx/(five *x^ two + three)
- dx divide by (5 multiply by x squared plus 3)
- dx divide by (five multiply by x to the power of two plus three)
- dx/(5*x2+3)
- dx/5*x2+3
- dx/(5*x²+3)
- dx/(5*x to the power of 2+3)
- dx/(5x^2+3)
- dx/(5x2+3)
- dx/5x2+3
- dx/5x^2+3
- dx divide by (5*x^2+3)
-
Similar expressions
- dx/(5*x^2-3)
Integral of dx/(5*x^2+3) dx
The solution
You have entered
[src]
1 / | | 1 | -------- dx | 2 | 5*x + 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{5 x^{2} + 3}\, dx$$
Integral(1/(5*x^2 + 3), (x, 0, 1))
Detail solution
We have the integral:
/ | | 1 | -------- dx | 2 | 5*x + 3 | /
Rewrite the integrand
1 1
-------- = ---------------------
2 / 2 \
5*x + 3 |/ ____ \ |
||-\/ 15 | |
3*||--------*x| + 1|
\\ 3 / /or
/ | | 1 | -------- dx | 2 = | 5*x + 3 | /
/
|
| 1
| ----------------- dx
| 2
| / ____ \
| |-\/ 15 |
| |--------*x| + 1
| \ 3 /
|
/
-----------------------
3 In the integral
/
|
| 1
| ----------------- dx
| 2
| / ____ \
| |-\/ 15 |
| |--------*x| + 1
| \ 3 /
|
/
-----------------------
3 do replacement
____
-x*\/ 15
v = ----------
3 then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
3 3 do backward replacement
/
|
| 1
| ----------------- dx
| 2
| / ____ \
| |-\/ 15 |
| |--------*x| + 1 / ____\
| \ 3 / ____ |x*\/ 15 |
| \/ 15 *atan|--------|
/ \ 3 /
----------------------- = ---------------------
3 15 Solution is:
/ ____\
____ |x*\/ 15 |
\/ 15 *atan|--------|
\ 3 /
C + ---------------------
15
The answer (Indefinite)
[src]
/ ____\ / ____ |x*\/ 15 | | \/ 15 *atan|--------| | 1 \ 3 / | -------- dx = C + --------------------- | 2 15 | 5*x + 3 | /
$$\int \frac{1}{5 x^{2} + 3}\, dx = C + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15} x}{3} \right)}}{15}$$
The graph
The answer
[src]
/ ____\
____ |\/ 15 |
\/ 15 *atan|------|
\ 3 /
-------------------
15
$$\frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{3} \right)}}{15}$$
=
=
/ ____\
____ |\/ 15 |
\/ 15 *atan|------|
\ 3 /
-------------------
15
$$\frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{3} \right)}}{15}$$
sqrt(15)*atan(sqrt(15)/3)/15
The graph
Use the examples entering the upper and lower limits of integration.