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How to use it?
- Integral of d{x}:
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Integral of e^x/x^2
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Integral of e^(x+1)
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Integral of 3^(2*x)
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Integral of (sinx-cosx)^2
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Identical expressions
- (sin(two x)-9cos(x))/(four (cos(x))^(2)-9sin(x)+ five)
- ( sinus of (2x) minus 9 co sinus of e of (x)) divide by (4( co sinus of e of (x)) to the power of (2) minus 9 sinus of (x) plus 5)
- ( sinus of (two x) minus 9 co sinus of e of (x)) divide by (four ( co sinus of e of (x)) to the power of (2) minus 9 sinus of (x) plus five)
- (sin(2x)-9cos(x))/(4(cos(x))(2)-9sin(x)+5)
- sin2x-9cosx/4cosx2-9sinx+5
- sin2x-9cosx/4cosx^2-9sinx+5
- (sin(2x)-9cos(x)) divide by (4(cos(x))^(2)-9sin(x)+5)
- (sin(2x)-9cos(x))/(4(cos(x))^(2)-9sin(x)+5)dx
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Similar expressions
- (sin(2x)-9cos(x))/(4(cos(x))^(2)+9sin(x)+5)
- (sin(2x)-9cos(x))/(4(cos(x))^(2)-9sin(x)-5)
- (sin(2x)+9cos(x))/(4(cos(x))^(2)-9sin(x)+5)
- (sin(2x)-9cosx)/(4(cosx)^(2)-9sinx+5)
Integral of (sin(2x)-9cos(x))/(4(cos(x))^(2)-9sin(x)+5) dx
The solution
You have entered
[src]
1 / | | sin(2*x) - 9*cos(x) | ------------------------ dx | 2 | 4*cos (x) - 9*sin(x) + 5 | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(2 x \right)} - 9 \cos{\left(x \right)}}{\left(- 9 \sin{\left(x \right)} + 4 \cos^{2}{\left(x \right)}\right) + 5}\, dx$$
Integral((sin(2*x) - 9*cos(x))/(4*cos(x)^2 - 9*sin(x) + 5), (x, 0, 1))
The answer (Indefinite)
[src]
/ / 2/x\\ / /x\ 2/x\\ | log|1 + tan |-|| log|3 - 8*tan|-| + 3*tan |-|| | sin(2*x) - 9*cos(x) \ \2// \ \2/ \2// / /x\ 2/x\\ | ------------------------ dx = C + ---------------- + ----------------------------- - log|3 + 2*tan|-| + 3*tan |-|| | 2 2 2 \ \2/ \2// | 4*cos (x) - 9*sin(x) + 5 | /
$$\int \frac{\sin{\left(2 x \right)} - 9 \cos{\left(x \right)}}{\left(- 9 \sin{\left(x \right)} + 4 \cos^{2}{\left(x \right)}\right) + 5}\, dx = C + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{2} + \frac{\log{\left(3 \tan^{2}{\left(\frac{x}{2} \right)} - 8 \tan{\left(\frac{x}{2} \right)} + 3 \right)}}{2} - \log{\left(3 \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 3 \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.