Question

вычислите неопределенный интеграл:

x^2*x^1/2 dx;

(8sin x - 9/cos^2 x)dx;

cos8x * sin 6x dx;

(4x-7)^6dx;

V(t)=3t^2-4t+1 .

Answer 1

1. $int{x^2sqrt{x}}, dx = int{x^{frac{5}{2}}}, dx = frac{2x^{frac{7}{2}}}{7}.$

2. $int{(8sinx-frac{9}{cos^2x})}, dx = -8cosx-9tgx.$

3. $int{cos8x*sin6x}, dx = frac{1}{2}int{sin14x}, dx - frac{1}{2}int{sin2x}, dx =$

= $-frac{1}{28}cos14x + frac{1}{4}cos2x = frac{1}{28}(7cos2x - cos14x).$

4. $int{(4x-7)^6}, dx = frac{1}{4}int{(4x-7)^6}, d(4x-7) = frac{1}{28}(4x-7)^7.$

5. $int{(3t^2-4t+1)}, dt = t^3-2t^2+t.$