Question

нужно сделать
3) ∫ x(m-1)dx
255 2) ∫ x3(1 - 6x2) dx
3) ∫ (3x-4 + 8x-5) dx;
4) ∫ (x-4 - x-3 - 3x 2 + 1) dx

Answer 1

254

$2)\int\limits {x}^{4} dx = \frac{ {x}^{5} }{5} + c \\$

$3)\int\limits {x}^{m - 1} dx = \frac{ {x}^{m - 1 + 1} }{m - 1 + 1} + C= \\ = \frac{ {x}^{m} }{m} + C$

255

$2)\int\limits {x}^{3} (1 - 6 {x}^{2})dx = \int\limits( {x}^{3} - 6 {x}^{5} )dx = \\ = \frac{ {x}^{4} }{4} - \frac{6 {x}^{6} } {6} + C= \frac{ {x}^{4} }{4} - {x}^{6} + c$

$3)\int\limits(3 {x}^{ - 4} + 8 {x}^{ - 5} )dx = \frac{3 {x}^{ - 3} }{ - 3} + \frac{8 {x}^{ - 4} }{( - 4)} + C = \\ = - \frac{1}{ {x}^{3} } - \frac{2}{ {x}^{4} } + C$

$4)\int\limits( {x}^{ - 4} - {x}^{ - 3} - 3 {x}^{ - 2} + 1)dx = \\ = \frac{ {x}^{ - 3} }{ - 3} - \frac{ {x}^{ - 2} }{( - 2)} - \frac{3 {x}^{ - 1} }{( - 1)} + x + C= \\ = - \frac{1}{3 {x}^{3} } + \frac{1}{2 {x}^{2} } + \frac{3}{x} + x + C$