Mister Exam
Least common denominator 4*x^(3/2)/3+2*sqrt(x)+x^5/5+e^(5*x^3+1)/15
The solution
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3 3/2 5 5*x + 1 4*x ___ x E ------ + 2*\/ x + -- + --------- 3 5 15
$$\frac{e^{5 x^{3} + 1}}{15} + \left(\frac{x^{5}}{5} + \left(2 \sqrt{x} + \frac{4 x^{\frac{3}{2}}}{3}\right)\right)$$
(4*x^(3/2))/3 + 2*sqrt(x) + x^5/5 + E^(5*x^3 + 1)/15
General simplification
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3
5 1 + 5*x 3/2
___ x e 4*x
2*\/ x + -- + --------- + ------
5 15 3
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{e^{5 x^{3} + 1}}{15}$$
2*sqrt(x) + x^5/5 + exp(1 + 5*x^3)/15 + 4*x^(3/2)/3
Common denominator
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3
5 3/2 5*x
___ x 4*x E*e
2*\/ x + -- + ------ + -------
5 3 15
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{e e^{5 x^{3}}}{15}$$
2*sqrt(x) + x^5/5 + 4*x^(3/2)/3 + E*exp(5*x^3)/15
Rational denominator
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3
5 3/2 ___ 1 + 5*x
3*x + 20*x + 30*\/ x + e
-------------------------------------
15
$$\frac{20 x^{\frac{3}{2}} + 30 \sqrt{x} + 3 x^{5} + e^{5 x^{3} + 1}}{15}$$
(3*x^5 + 20*x^(3/2) + 30*sqrt(x) + exp(1 + 5*x^3))/15
Combinatorics
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3
5 3/2 5*x
___ x 4*x E*e
2*\/ x + -- + ------ + -------
5 3 15
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{e e^{5 x^{3}}}{15}$$
2*sqrt(x) + x^5/5 + 4*x^(3/2)/3 + E*exp(5*x^3)/15
Powers
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3
5 1 + 5*x 3/2
___ x e 4*x
2*\/ x + -- + --------- + ------
5 15 3
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{e^{5 x^{3} + 1}}{15}$$
2*sqrt(x) + x^5/5 + exp(1 + 5*x^3)/15 + 4*x^(3/2)/3
Numerical answer
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2.0*x^0.5 + 0.2*x^5 + 0.0666666666666667*2.71828182845905^(1.0 + 5.0*x^3) + 1.33333333333333*x^1.5
2.0*x^0.5 + 0.2*x^5 + 0.0666666666666667*2.71828182845905^(1.0 + 5.0*x^3) + 1.33333333333333*x^1.5
Trigonometric part
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3
5 1 + 5*x 3/2
___ x (cosh(1) + sinh(1)) 4*x
2*\/ x + -- + --------------------------- + ------
5 15 3
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{5 x^{3} + 1}}{15}$$
3
5 1 + 5*x 3/2
___ x e 4*x
2*\/ x + -- + --------- + ------
5 15 3
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{e^{5 x^{3} + 1}}{15}$$
5 / 3\ / 3\ 3/2
___ x cosh\1 + 5*x / sinh\1 + 5*x / 4*x
2*\/ x + -- + -------------- + -------------- + ------
5 15 15 3
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{\sinh{\left(5 x^{3} + 1 \right)}}{15} + \frac{\cosh{\left(5 x^{3} + 1 \right)}}{15}$$
2*sqrt(x) + x^5/5 + cosh(1 + 5*x^3)/15 + sinh(1 + 5*x^3)/15 + 4*x^(3/2)/3
Assemble expression
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3
5 5*x + 1 3/2
___ x e 4*x
2*\/ x + -- + --------- + ------
5 15 3
$$\frac{4 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{5}}{5} + \frac{e^{5 x^{3} + 1}}{15}$$
2*sqrt(x) + x^5/5 + exp(5*x^3 + 1)/15 + 4*x^(3/2)/3
Combining rational expressions
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3
5 ___ 1 + 5*x
3*x + 10*\/ x *(3 + 2*x) + e
-------------------------------------
15
$$\frac{10 \sqrt{x} \left(2 x + 3\right) + 3 x^{5} + e^{5 x^{3} + 1}}{15}$$
(3*x^5 + 10*sqrt(x)*(3 + 2*x) + exp(1 + 5*x^3))/15