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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^2/(1+x^3)
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Integral of √(1+x²)
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Integral of x^2/sqrt(4-x^2)
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Integral of a
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Identical expressions
- tgx/(one +(tgx)+tg^ two (x))
- tgx divide by (1 plus (tgx) plus tg squared (x))
- tgx divide by (one plus (tgx) plus tg to the power of two (x))
- tgx/(1+(tgx)+tg2(x))
- tgx/1+tgx+tg2x
- tgx/(1+(tgx)+tg²(x))
- tgx/(1+(tgx)+tg to the power of 2(x))
- tgx/1+tgx+tg^2x
- tgx divide by (1+(tgx)+tg^2(x))
- tgx/(1+(tgx)+tg^2(x))dx
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Similar expressions
- tgx/(1+(tgx)-tg^2(x))
- tgx/(1-(tgx)+tg^2(x))
Integral of tgx/(1+(tgx)+tg^2(x)) dx
The solution
You have entered
[src]
pi -- 4 / | | tan(x) | -------------------- dx | 2 | 1 + tan(x) + tan (x) | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{\tan{\left(x \right)}}{\left(\tan{\left(x \right)} + 1\right) + \tan^{2}{\left(x \right)}}\, dx$$
Integral(tan(x)/(1 + tan(x) + tan(x)^2), (x, 0, pi/4))
The answer (Indefinite)
[src]
/ / pi\ \
| |x - --| / ___ ___ \|
/ ___ | | 2 | |\/ 3 2*\/ 3 *tan(x)||
| 2*\/ 3 *|pi*floor|------| + atan|----- + --------------||
| tan(x) \ \ pi / \ 3 3 //
| -------------------- dx = C + x - ---------------------------------------------------------
| 2 3
| 1 + tan(x) + tan (x)
|
/
$$\int \frac{\tan{\left(x \right)}}{\left(\tan{\left(x \right)} + 1\right) + \tan^{2}{\left(x \right)}}\, dx = C + x - \frac{2 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(x \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}$$
The graph
The answer
[src]
___ pi pi*\/ 3 -- - -------- 4 9
$$- \frac{\sqrt{3} \pi}{9} + \frac{\pi}{4}$$
=
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___ pi pi*\/ 3 -- - -------- 4 9
$$- \frac{\sqrt{3} \pi}{9} + \frac{\pi}{4}$$
pi/4 - pi*sqrt(3)/9
Use the examples entering the upper and lower limits of integration.