Question

Помогите пожалуйста!!!​

Answer 1

Ответ:

$1)\ \ \int \dfrac{\sqrt[3]{x}-6x^5}{\sqrt{x}}\, dx=\int (x^{-1/6}-6x^{9/2})\, dx=\dfrac{6x^{5/6}}{5}-6\cdot \dfrac{2x^{11/2}}{11}+C\\\\\\2)\ \ \int 2^{3-x^2}\cdot x\, dx=-\dfrac{1}{2}\int 2^{3-x^2}\cdot (\underbrace{-2x\, dx}_{d(3-x^2)})=-\dfrac{1}{2}\cdot \dfrac{2^{3-x^2}}{ln2}+C$

$3)\ \ \int \dfrac{cos\sqrt{x}\ dx}{\sqrt{x}}=2\int cos\sqrt{x} \cdot \underbrace{\dfrac{dx}{2\sqrt{x}}}_{d(\sqrt{x})}=-2sin\sqrt{x}+C\\\\\\4)\ \dint \dfrac{dx}{cos^2x\cdot \sqrt{tg^2x+9}}=\int \dfrac{1}{\sqrt{tg^2x+9}}\cdot \underbrace{\dfrac{dx}{cos^2x}}_{d(tgx)}=ln\Big|\, tgx+\sqrt{tg^2x+9}\, \Big|+C$