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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*e^3x
- Integral of x*atan(x)/sqrt(1+x^3)
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Integral of x^2*e^(x/2)*dx
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Integral of x^2*(9-x^2)^(-1/2)
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Identical expressions
- five ^(2x)*cos(5x)
- 5 to the power of (2x) multiply by co sinus of e of (5x)
- five to the power of (2x) multiply by co sinus of e of (5x)
- 5(2x)*cos(5x)
- 52x*cos5x
- 5^(2x)cos(5x)
- 5(2x)cos(5x)
- 52xcos5x
- 5^2xcos5x
- 5^(2x)*cos(5x)dx
Integral of 5^(2x)*cos(5x) dx
The solution
You have entered
[src]
1 / | | 2*x | 5 *cos(5*x) dx | / 0
$$\int\limits_{0}^{1} 5^{2 x} \cos{\left(5 x \right)}\, dx$$
Integral(5^(2*x)*cos(5*x), (x, 0, 1))
The answer (Indefinite)
[src]
/ | 2*x 2*x | 2*x 5*5 *sin(5*x) 2*5 *cos(5*x)*log(5) | 5 *cos(5*x) dx = C + --------------- + ---------------------- | 2 2 / 25 + 4*log (5) 25 + 4*log (5)
$${{5\,e^{2\,\log 5\,x}\,\sin \left(5\,x\right)+2\,\log 5\,e^{2\,
\log 5\,x}\,\cos \left(5\,x\right)}\over{4\,\left(\log 5\right)^2+25
}}$$
The graph
The answer
[src]
2*log(5) 125*sin(5) 50*cos(5)*log(5)
- -------------- + -------------- + ----------------
2 2 2
25 + 4*log (5) 25 + 4*log (5) 25 + 4*log (5)
$${{125\,\sin 5+50\,\cos 5\,\log 5}\over{4\,\left(\log 5\right)^2+25
}}-{{2\,\log 5}\over{4\,\left(\log 5\right)^2+25}}$$
=
=
2*log(5) 125*sin(5) 50*cos(5)*log(5)
- -------------- + -------------- + ----------------
2 2 2
25 + 4*log (5) 25 + 4*log (5) 25 + 4*log (5)
$$\frac{125 \sin{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25} - \frac{2 \log{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25} + \frac{50 \log{\left(5 \right)} \cos{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25}$$
The graph
Use the examples entering the upper and lower limits of integration.