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How to use it?
- Integral of d{x}:
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Integral of 1/(sqrt(4-9x^2))
- Integral of (x+4)/(x^2(x-1))
- Integral of sqrt(x^2+6)
- Integral of sqrt(arctg(x))
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Identical expressions
- (cos(zero .5x+ zero .1 two 5x^ two))^2
- ( co sinus of e of (0.5x plus 0.125x squared )) squared
- ( co sinus of e of (zero .5x plus zero .1 two 5x to the power of two)) squared
- (cos(0.5x+0.125x2))2
- cos0.5x+0.125x22
- (cos(0.5x+0.125x²))²
- (cos(0.5x+0.125x to the power of 2)) to the power of 2
- cos0.5x+0.125x^2^2
- (cos(0.5x+0.125x^2))^2dx
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Similar expressions
- (cos(0.5x-0.125x^2))^2
Integral of (cos(0.5x+0.125x^2))^2 dx
The solution
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[src]
157 --- 50 / | | / 2\ | 2|x x | | cos |- + --| dx | \2 8 / | / 0
$$\int\limits_{0}^{\frac{157}{50}} \cos^{2}{\left(\frac{x^{2}}{8} + \frac{x}{2} \right)}\, dx$$
Integral(cos(x/2 + x^2/8)^2, (x, 0, 157/50))
The answer (Indefinite)
[src]
/ / ___ / x\\ / ___ / x\\ \
| |\/ 2 *|1 + -|| |\/ 2 *|1 + -|| |
/ ___ ____ | | \ 2/| | \ 2/| |
| \/ 2 *\/ pi *|cos(1)*C|-------------| + S|-------------|*sin(1)|
| / 2\ | | ____ | | ____ | |
| 2|x x | x \ \ \/ pi / \ \/ pi / /
| cos |- + --| dx = C + - + ----------------------------------------------------------------
| \2 8 / 2 2
|
/
$$\int \cos^{2}{\left(\frac{x^{2}}{8} + \frac{x}{2} \right)}\, dx = C + \frac{x}{2} + \frac{\sqrt{2} \sqrt{\pi} \left(\cos{\left(1 \right)} C\left(\frac{\sqrt{2} \left(\frac{x}{2} + 1\right)}{\sqrt{\pi}}\right) + \sin{\left(1 \right)} S\left(\frac{\sqrt{2} \left(\frac{x}{2} + 1\right)}{\sqrt{\pi}}\right)\right)}{2}$$
The graph
The answer
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/ / ___ \ / ___ \ \ / / ___ \ / ___ \ \
___ ____ | |257*\/ 2 | |257*\/ 2 | | ___ ____ | |\/ 2 | |\/ 2 | |
\/ 2 *\/ pi *|cos(1)*C|----------| + S|----------|*sin(1)| \/ 2 *\/ pi *|cos(1)*C|------| + S|------|*sin(1)|
| | ____| | ____| | | | ____| | ____| |
157 \ \100*\/ pi / \100*\/ pi / / \ \\/ pi / \\/ pi / /
--- + ---------------------------------------------------------- - --------------------------------------------------
100 2 2
$$- \frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(1 \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(1 \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2} + \frac{\sqrt{2} \sqrt{\pi} \left(\cos{\left(1 \right)} C\left(\frac{257 \sqrt{2}}{100 \sqrt{\pi}}\right) + \sin{\left(1 \right)} S\left(\frac{257 \sqrt{2}}{100 \sqrt{\pi}}\right)\right)}{2} + \frac{157}{100}$$
=
=
/ / ___ \ / ___ \ \ / / ___ \ / ___ \ \
___ ____ | |257*\/ 2 | |257*\/ 2 | | ___ ____ | |\/ 2 | |\/ 2 | |
\/ 2 *\/ pi *|cos(1)*C|----------| + S|----------|*sin(1)| \/ 2 *\/ pi *|cos(1)*C|------| + S|------|*sin(1)|
| | ____| | ____| | | | ____| | ____| |
157 \ \100*\/ pi / \100*\/ pi / / \ \\/ pi / \\/ pi / /
--- + ---------------------------------------------------------- - --------------------------------------------------
100 2 2
$$- \frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(1 \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(1 \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2} + \frac{\sqrt{2} \sqrt{\pi} \left(\cos{\left(1 \right)} C\left(\frac{257 \sqrt{2}}{100 \sqrt{\pi}}\right) + \sin{\left(1 \right)} S\left(\frac{257 \sqrt{2}}{100 \sqrt{\pi}}\right)\right)}{2} + \frac{157}{100}$$
157/100 + sqrt(2)*sqrt(pi)*(cos(1)*fresnelc(257*sqrt(2)/(100*sqrt(pi))) + fresnels(257*sqrt(2)/(100*sqrt(pi)))*sin(1))/2 - sqrt(2)*sqrt(pi)*(cos(1)*fresnelc(sqrt(2)/sqrt(pi)) + fresnels(sqrt(2)/sqrt(pi))*sin(1))/2
Use the examples entering the upper and lower limits of integration.