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- Improper integral
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How to use it?
- Integral of d{x}:
- Integral of √(a^2-x^2)
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Integral of exp(7*x)*sin(x)
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Integral of cos^4(2x)
- Integral of e^(-x)/x
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Identical expressions
- one / one +sinx+cosx
- 1 divide by 1 plus sinus of x plus co sinus of e of x
- one divide by one plus sinus of x plus co sinus of e of x
- 1 divide by 1+sinx+cosx
- 1/1+sinx+cosxdx
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Similar expressions
- 1/((1+sinx+cosx)^2)
- 1/1-sinx+cosx
- 1/(1+sinx+cosx)
- 1/1+sinx-cosx
- 1/(1+sin(x)+cos(x))
Integral of 1/1+sinx+cosx dx
The solution
You have entered
[src]
0 / | | (1 + sin(x) + cos(x)) dx | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{0} \left(\sin{\left(x \right)} + \cos{\left(x \right)} + 1\right)\, dx$$
Integral(1 + sin(x) + cos(x), (x, pi/2, 0))
Detail solution
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Integrate term-by-term:
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The integral of sine is negative cosine:
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The integral of cosine is sine:
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The integral of a constant is the constant times the variable of integration:
The result is:
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Now simplify:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ | | (1 + sin(x) + cos(x)) dx = C + x - cos(x) + sin(x) | /
$$\sin x-\cos x+x$$
The graph
The answer
[src]
pi
-2 - --
2
$$-{{\pi+2\,\sin \left({{\pi}\over{2}}\right)-2\,\cos \left({{\pi
}\over{2}}\right)+2}\over{2}}$$
=
=
pi
-2 - --
2
$$-2 - \frac{\pi}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.