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How to use it?
- Integral of d{x}:
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Integral of 1/√(1-4x^2)
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Integral of x(x^2+3)dx
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Integral of xcos(3x)
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Integral of x*cos(x^3)
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Identical expressions
- x*cos(x^ three)
- x multiply by co sinus of e of (x cubed )
- x multiply by co sinus of e of (x to the power of three)
- x*cos(x3)
- x*cosx3
- x*cos(x³)
- x*cos(x to the power of 3)
- xcos(x^3)
- xcos(x3)
- xcosx3
- xcosx^3
- x*cos(x^3)dx
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Similar expressions
- xcosx^3
- sinx*(cosx)^3
Integral of x*cos(x^3) dx
The solution
You have entered
[src]
1 / | | / 3\ | x*cos\x / dx | / 0
$$\int\limits_{0}^{1} x \cos{\left(x^{3} \right)}\, dx$$
Integral(x*cos(x^3), (x, 0, 1))
The answer (Indefinite)
[src]
_ / | 6 \
/ 2 |_ | 1/3 | -x |
| x *Gamma(1/3)* | | | ----|
| / 3\ 1 2 \1/2, 4/3 | 4 /
| x*cos\x / dx = C + ------------------------------------
| 6*Gamma(4/3)
/
$$\int x \cos{\left(x^{3} \right)}\, dx = C + \frac{x^{2} \Gamma\left(\frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{x^{6}}{4}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
The graph
The answer
[src]
_
|_ / 1/3 | \
Gamma(1/3)* | | | -1/4|
1 2 \1/2, 4/3 | /
---------------------------------
6*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_
|_ / 1/3 | \
Gamma(1/3)* | | | -1/4|
1 2 \1/2, 4/3 | /
---------------------------------
6*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
gamma(1/3)*hyper((1/3,), (1/2, 4/3), -1/4)/(6*gamma(4/3))
The graph
Use the examples entering the upper and lower limits of integration.