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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^(-1/2)
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Integral of 1/sqrt(1+u^2)
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Integral of x^4lnx
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Integral of x*dx/(x^2-1)
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Identical expressions
- one /(sin(4x)+ three)
- 1 divide by ( sinus of (4x) plus 3)
- one divide by ( sinus of (4x) plus three)
- 1/sin4x+3
- 1 divide by (sin(4x)+3)
- 1/(sin(4x)+3)dx
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Similar expressions
- 1/(sin(4x)-3)
Integral of 1/(sin(4x)+3) dx
The solution
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[src]
1 / | | 1 | ------------ dx | sin(4*x) + 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(4 x \right)} + 3}\, dx$$
Integral(1/(sin(4*x) + 3), (x, 0, 1))
The answer (Indefinite)
[src]
/ / pi\ \
| |2*x - --| / ___ ___ \|
/ ___ | | 2 | |\/ 2 3*\/ 2 *tan(2*x)||
| \/ 2 *|pi*floor|--------| + atan|----- + ----------------||
| 1 \ \ pi / \ 4 4 //
| ------------ dx = C + -----------------------------------------------------------
| sin(4*x) + 3 8
|
/
$$\int \frac{1}{\sin{\left(4 x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(2 x \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{2 x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{8}$$
The graph
The answer
[src]
/ / ___\\ / ___ ___ \
___ | |\/ 2 || ___ |\/ 2 3*\/ 2 *tan(2)|
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|----- + --------------|
\ \ 4 // \ 4 4 /
- ------------------------- + ----------------------------------
8 8
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(2 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{8} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{8}$$
=
=
/ / ___\\ / ___ ___ \
___ | |\/ 2 || ___ |\/ 2 3*\/ 2 *tan(2)|
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|----- + --------------|
\ \ 4 // \ 4 4 /
- ------------------------- + ----------------------------------
8 8
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(2 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{8} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{8}$$
-sqrt(2)*(-pi + atan(sqrt(2)/4))/8 + sqrt(2)*atan(sqrt(2)/4 + 3*sqrt(2)*tan(2)/4)/8
Use the examples entering the upper and lower limits of integration.