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Problem ∫ x ( 1 + x 1 / 3 ) 4 d x \int \sqrt{x}(1+x^{1/3})^4\,dx ∫ x ( 1 + x 1/3 ) 4 d x is equal to
(a) 2 { x 2 / 3 + 4 11 x 11 / 6 + 6 13 x 13 / 6 + 4 15 x 5 / 2 + 1 17 x 17 / 6 } + c 2\left\{x^{2/3} + \frac{4}{11}x^{11/6} + \frac{6}{13}x^{13/6} + \frac{4}{15}x^{5/2} + \frac{1}{17}x^{17/6}\right\} + c 2 { x 2/3 + 11 4 x 11/6 + 13 6 x 13/6 + 15 4 x 5/2 + 17 1 x 17/6 } + c
(b) 6 { x 2 / 3 − 4 11 x 11 / 6 + 6 13 x 13 / 6 − 4 15 x 5 / 2 + 1 17 x 17 / 6 } + c 6\left\{x^{2/3} - \frac{4}{11}x^{11/6} + \frac{6}{13}x^{13/6} - \frac{4}{15}x^{5/2} + \frac{1}{17}x^{17/6}\right\} + c 6 { x 2/3 − 11 4 x 11/6 + 13 6 x 13/6 − 15 4 x 5/2 + 17 1 x 17/6 } + c
(c) 6 { x 2 / 3 + 4 11 x 11 / 6 + 6 13 x 13 / 6 + 4 15 x 5 / 2 + 1 17 x 17 / 6 } + c 6\left\{x^{2/3} + \frac{4}{11}x^{11/6} + \frac{6}{13}x^{13/6} + \frac{4}{15}x^{5/2} + \frac{1}{17}x^{17/6}\right\} + c 6 { x 2/3 + 11 4 x 11/6 + 13 6 x 13/6 + 15 4 x 5/2 + 17 1 x 17/6 } + c
(d) None of these
(a) 2 { x 2 / 3 + 4 11 x 11 / 6 + 6 13 x 13 / 6 + 4 15 x 5 / 2 + 1 17 x 17 / 6 } + c 2\left\{x^{2/3} + \frac{4}{11}x^{11/6} + \frac{6}{13}x^{13/6} + \frac{4}{15}x^{5/2} + \frac{1}{17}x^{17/6}\right\} + c 2 { x 2/3 + 11 4 x 11/6 + 13 6 x 13/6 + 15 4 x 5/2 + 17 1 x 17/6 } + c
(b) 6 { x 2 / 3 − 4 11 x 11 / 6 + 6 13 x 13 / 6 − 4 15 x 5 / 2 + 1 17 x 17 / 6 } + c 6\left\{x^{2/3} - \frac{4}{11}x^{11/6} + \frac{6}{13}x^{13/6} - \frac{4}{15}x^{5/2} + \frac{1}{17}x^{17/6}\right\} + c 6 { x 2/3 − 11 4 x 11/6 + 13 6 x 13/6 − 15 4 x 5/2 + 17 1 x 17/6 } + c
(c) 6 { x 2 / 3 + 4 11 x 11 / 6 + 6 13 x 13 / 6 + 4 15 x 5 / 2 + 1 17 x 17 / 6 } + c 6\left\{x^{2/3} + \frac{4}{11}x^{11/6} + \frac{6}{13}x^{13/6} + \frac{4}{15}x^{5/2} + \frac{1}{17}x^{17/6}\right\} + c 6 { x 2/3 + 11 4 x 11/6 + 13 6 x 13/6 + 15 4 x 5/2 + 17 1 x 17/6 } + c
(d) None of these
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