Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of e^(4*x)*dx
-
Integral of 1/6x
-
Integral of x/(sinx^2)^2
-
Integral of x*ln(x^2+1)
-
Identical expressions
- (one -x^ four)^(one / four)
- (1 minus x to the power of 4) to the power of (1 divide by 4)
- (one minus x to the power of four) to the power of (one divide by four)
- (1-x4)(1/4)
- 1-x41/4
- (1-x⁴)^(1/4)
- 1-x^4^1/4
- (1-x^4)^(1 divide by 4)
- (1-x^4)^(1/4)dx
-
Similar expressions
- (1+x^4)^(1/4)
Integral of (1-x^4)^(1/4) dx
The solution
You have entered
[src]
1 / | | ________ | 4 / 4 | \/ 1 - x dx | / -1
$$\int\limits_{-1}^{1} \sqrt[4]{1 - x^{4}}\, dx$$
Integral((1 - x^4)^(1/4), (x, -1, 1))
The answer (Indefinite)
[src]
/ _ | |_ /-1/4, 1/4 | 4 2*pi*I\ | ________ x*Gamma(1/4)* | | | x *e | | 4 / 4 2 1 \ 5/4 | / | \/ 1 - x dx = C + ------------------------------------------ | 4*Gamma(5/4) /
$$\int \sqrt[4]{1 - x^{4}}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
The graph
The answer
[src]
_
|_ /-1/4, 1/4 | \
Gamma(1/4)* | | | 1|
2 1 \ 5/4 | /
-------------------------------
2*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}$$
=
=
_
|_ /-1/4, 1/4 | \
Gamma(1/4)* | | | 1|
2 1 \ 5/4 | /
-------------------------------
2*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.