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How to use it?
- Integral of d{x}:
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Integral of tan^3(x)dx
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Integral of e^cos(x)*sin(x)
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Integral of dx/(2+x^2)
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Integral of e^x*sin(2x)
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Identical expressions
- sqrt(one + nine *x^(four))
- square root of (1 plus 9 multiply by x to the power of (4))
- square root of (one plus nine multiply by x to the power of (four))
- √(1+9*x^(4))
- sqrt(1+9*x(4))
- sqrt1+9*x4
- sqrt(1+9x^(4))
- sqrt(1+9x(4))
- sqrt1+9x4
- sqrt1+9x^4
- sqrt(1+9*x^(4))dx
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Similar expressions
- sqrt(1-9*x^(4))
Integral of sqrt(1+9*x^(4)) dx
The solution
You have entered
[src]
8 / | | __________ | / 4 | \/ 1 + 9*x dx | / 1
$$\int\limits_{1}^{8} \sqrt{9 x^{4} + 1}\, dx$$
Integral(sqrt(1 + 9*x^4), (x, 1, 8))
The answer (Indefinite)
[src]
/ _ | |_ /-1/2, 1/4 | 4 pi*I\ | __________ x*Gamma(1/4)* | | | 9*x *e | | / 4 2 1 \ 5/4 | / | \/ 1 + 9*x dx = C + ------------------------------------------ | 4*Gamma(5/4) /
$$\int \sqrt{9 x^{4} + 1}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9 x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
The graph
The answer
[src]
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|_ /-1/2, 1/4 | pi*I\ |_ /-1/2, 1/4 | pi*I\
2*Gamma(1/4)* | | | 36864*e | Gamma(1/4)* | | | 9*e |
2 1 \ 5/4 | / 2 1 \ 5/4 | /
------------------------------------------- - -------------------------------------
Gamma(5/4) 4*Gamma(5/4)
$$- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{2 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {36864 e^{i \pi}} \right)}}{\Gamma\left(\frac{5}{4}\right)}$$
=
=
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|_ /-1/2, 1/4 | pi*I\ |_ /-1/2, 1/4 | pi*I\
2*Gamma(1/4)* | | | 36864*e | Gamma(1/4)* | | | 9*e |
2 1 \ 5/4 | / 2 1 \ 5/4 | /
------------------------------------------- - -------------------------------------
Gamma(5/4) 4*Gamma(5/4)
$$- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{2 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {36864 e^{i \pi}} \right)}}{\Gamma\left(\frac{5}{4}\right)}$$
2*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 36864*exp_polar(pi*i))/gamma(5/4) - gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 9*exp_polar(pi*i))/(4*gamma(5/4))
Use the examples entering the upper and lower limits of integration.