Question

Помогите пожалуйста срочно нужно!!!!!! Дам 55 баллов!!!

Answer 1

2.

$\int\limits( \frac{ {x}^{ - 7} }{6} - \frac{5}{4} {x}^{4} )dx = \\ = \frac{ {x}^{ - 6} }{6 \times ( - 6)} - \frac{5}{4} \times \frac{ {x}^{5} } {5 } + C = \\ = - \frac{1}{36 {x}^{6} } - \frac{ {x}^{5} }{4} + C$

4.

$\int\limits(15 {x}^{24} - \frac{28}{ \sqrt{6 - 7x} } )dx = \\ = 15 \times \frac{ {x}^{25 } }{25} + \int\limits \frac{4 \times ( - 7)dx}{ \sqrt{6 - 7 x } } = \\ = \frac{3 {x}^{25} }{5} + 4\int\limits \frac{d(6 - 7x)}{ {(6 - 7x)}^{ \frac{1}{2} } } = \\ = \frac{3 {x}^{25} }{5} + 4 \times \frac{ {(6 - 7x)}^{ \frac{1}{2} } }{ \frac{1}{2} } + C= \\ = \frac{3 {x}^{25} }{5} + 8 \sqrt{6 - 7x} + C$

2.

$\int\limits27 \cos(9x)dx =\int\limits3 \times 9 \cos(9x) dx = \\ = 3\int\limits\cos(9x) d(9x) = 3 \sin(9x) + C$

4.

$\int\limits \frac{20dx}{ \sin {}^{2} (2.5x) } = \int\limits \frac{8 \times 2.5dx}{ \sin {}^{2} (2.5x) } = \\ = 8\int\limits \frac{d(2.5x)}{ \sin {}^{2} (2.5x) } = - 8ctg(2.5x) + C$

2.

$F(x) = \int\limits {(3x - 2)}^{8} dx = \frac{1}{3} \int\limits {(3x - 2)}^{8} d(3x) = \\ = \frac{1}{3} \int\limits {(3x - 2)}^{8} d(3x - 2) = \\ = \frac{1}{3} \times \frac{ {(3x - 2)}^{9} }{9} +C = \frac{ {(3x - 2)}^{9} }{27} + C$

4.

$F(x) = \int\limits \cos(2x + \frac{\pi}{3} ) = \frac{1}{2} \int\limits \cos((2x + \frac{\pi}{3} ) d(2x + \frac{\pi}{3} ) = \\ = \frac{1}{2} \sin(2x + \frac{\pi}{3} ) + C$

2.

$F(x) = \int\limits \frac{1}{ \sin(3x - \frac{\pi}{8} ) } dx = \frac{1}{3} \int\limits \frac{d(3x - \frac{\pi}{8}) }{ \sin(3x - \frac{\pi}{8} ) } = \\ = - \frac{1}{3} ctg(3x - \frac{\pi}{8} ) + C$

4.

$F(x) = \int\limits(1 + \frac{6}{ \cos {}^{2} ( \frac{x}{6} - \frac{\pi}{5} ) } )dx = \\ = \int\limits \: dx + 6 \times 6\int\limits \frac{ d( \frac{x}{6} - \frac{\pi}{5}) }{ \cos {}^{2} ( \frac{x}{6} - \frac{\pi}{5} ) } = \\ = x + 36tg( \frac{x}{6} - \frac{\pi}{5} ) + C$

2.

$F(x) = \int\limits( \frac{1}{2 \sqrt{x - 5} } + \cos(2 + \frac{x}{3} ) )dx = \\ = \frac{1}{2} \int\limits \frac{d(x - 5)}{ \sqrt{x - 5} } + 3\int\limits \cos(2 + \frac{x}{3} ) d(2 + \frac{x}{3} ) = \\ = \frac{1} {2} \times \frac{ {(x - 5)}^{ \frac{1}{2} } }{ \frac{1}{2} } + 3 \sin(2 + \frac{x} {3} ) + C = \\ = \sqrt{x - 5} + 3 \sin(2 + \frac{x}{3} ) + C$

4.

$F(x) = \int\limits \frac{4}{5 \sqrt{2 + 3x} } - \frac{1}{ {(2 - x)}^{4} } )dx = \\ = \frac{4}{5} \times \frac{1}{3} \int\limits \frac{d(3x + 2)}{ \sqrt{3x + 2} } + \int\limits \frac{d(2 - x)}{ {(2 - x)}^{4} } = \\ = \frac{4}{15} \times \frac{ {(3x + 2)}^{ \frac{1}{2} } }{ \frac{1}{2} } + \frac{ {(2 - x)}^{ - 3} }{( - 3)} + C = \\ = \frac{8} {15} \sqrt{3x + 2} - \frac{1}{3 {(2 - x)}^{3} } + C$

2.

$F(x) = \int\limits \sin( \frac{x}{4} ) \cos( \frac{x}{4} ) dx = \\ = \frac{1}{2}\int\limits2\sin( \frac{x}{4} ) \cos( \frac{x} {4} ) dx = \\ = \frac{1}{2} \int\limits\sin( \frac{x}{2} ) dx = \int\limits \sin( \frac{x}{2} ) d( \frac{x}{2} ) = \\ = - \cos( \frac{x}{2} ) + C$

4.

$F(x) = \int\limits(1 - 2 \sin {}^{2} ( \frac{x}{6} ) )dx = \int\limits \cos( \frac{x}{3} ) dx = \\ = 3 \sin( \frac{x}{3} ) + C$