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- Integral of d{x}:
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Integral of cosx^2
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Integral of sinh(x)
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Integral of 6x^5
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Integral of z
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Identical expressions
- (two x^ four +x+sin3x)/(3x^ five -x^2+ seven)
- (2x to the power of 4 plus x plus sinus of 3x) divide by (3x to the power of 5 minus x squared plus 7)
- (two x to the power of four plus x plus sinus of 3x) divide by (3x to the power of five minus x squared plus seven)
- (2x4+x+sin3x)/(3x5-x2+7)
- 2x4+x+sin3x/3x5-x2+7
- (2x⁴+x+sin3x)/(3x⁵-x²+7)
- (2x to the power of 4+x+sin3x)/(3x to the power of 5-x to the power of 2+7)
- 2x^4+x+sin3x/3x^5-x^2+7
- (2x^4+x+sin3x) divide by (3x^5-x^2+7)
- (2x^4+x+sin3x)/(3x^5-x^2+7)dx
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Similar expressions
- (2x^4-x+sin3x)/(3x^5-x^2+7)
- (2x^4+x-sin3x)/(3x^5-x^2+7)
- (2x^4+x+sin3x)/(3x^5+x^2+7)
- (2x^4+x+sin3x)/(3x^5-x^2-7)
Integral of (2x^4+x+sin3x)/(3x^5-x^2+7) dx
The solution
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[src]
1 / | | 4 | 2*x + x + sin(3*x) | ------------------- dx | 5 2 | 3*x - x + 7 | / 0
$$\int\limits_{0}^{1} \frac{\left(2 x^{4} + x\right) + \sin{\left(3 x \right)}}{\left(3 x^{5} - x^{2}\right) + 7}\, dx$$
Integral((2*x^4 + x + sin(3*x))/(3*x^5 - x^2 + 7), (x, 0, 1))
The answer (Indefinite)
[src]
/ | / | 4 / / 4 2 3\\ | / / 4 3 2 \\ | 2*x + x + sin(3*x) | 5 4 3 2 | 18375 6511567725*t 260463789*t 9646891*t 434104515*t || | sin(3*x) | 5 3 2 | 19 12862356*t 3215589*t 12*t t || | ------------------- dx = C + 2*RootSum|260462709*t - 86820903*t + 11576142*t - 771746*t + 25725*t - 343, t -> t*log|- ----- + x - ------------- - ------------ + --------- + ------------|| + | ------------- dx + RootSum|9646767*t + 45*t - 5*t - 5*t + 1, t -> t*log|--- + x - ----------- - ---------- - ----- - --|| | 5 2 \ \ 8 28 56 56 8 // | 2 5 \ \525 175 175 35 21// | 3*x - x + 7 | 7 - x + 3*x | | / /
$$\int \frac{\left(2 x^{4} + x\right) + \sin{\left(3 x \right)}}{\left(3 x^{5} - x^{2}\right) + 7}\, dx = C + \int \frac{\sin{\left(3 x \right)}}{3 x^{5} - x^{2} + 7}\, dx + \operatorname{RootSum} {\left(9646767 t^{5} + 45 t^{3} - 5 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(- \frac{12862356 t^{4}}{175} - \frac{3215589 t^{3}}{175} - \frac{12 t^{2}}{35} - \frac{t}{21} + x + \frac{19}{525} \right)} \right)\right)} + 2 \operatorname{RootSum} {\left(260462709 t^{5} - 86820903 t^{4} + 11576142 t^{3} - 771746 t^{2} + 25725 t - 343, \left( t \mapsto t \log{\left(- \frac{6511567725 t^{4}}{28} + \frac{434104515 t^{3}}{8} - \frac{260463789 t^{2}}{56} + \frac{9646891 t}{56} + x - \frac{18375}{8} \right)} \right)\right)}$$
Use the examples entering the upper and lower limits of integration.