Упр.363 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

2) (3x-2) корень 3 степени x;
3) x+4/ корень 3 степени x;
4) x-3/корень x.

1. $$f(x)=(2x+1)\sqrt{x}=2x^{\frac32}+x^{\frac12}$$

   $$F(x)=\int \left(2x^{\frac32}+x^{\frac12}\right)\,dx =2\cdot \frac{x^{\frac52}}{\frac52}+\frac{x^{\frac32}}{\frac32}+C =\frac45x^{\frac52}+\frac23x^{\frac32}+C$$

2. $$f(x)=(3x-2)\sqrt[3]{x}=3x^{\frac43}-2x^{\frac13}$$

   $$F(x)=\int \left(3x^{\frac43}-2x^{\frac13}\right)\,dx =3\cdot \frac{x^{\frac73}}{\frac73}-2\cdot \frac{x^{\frac43}}{\frac43}+C =\frac97x^{\frac73}-\frac32x^{\frac43}+C$$

3. $$f(x)=\frac{x+4}{\sqrt[3]{x}}=x^{\frac23}+4x^{-\frac13}$$

   $$F(x)=\int \left(x^{\frac23}+4x^{-\frac13}\right)\,dx =\frac{x^{\frac53}}{\frac53}+4\cdot \frac{x^{\frac23}}{\frac23}+C =\frac35x^{\frac53}+6x^{\frac23}+C$$

4. $$f(x)=\frac{x-3}{\sqrt{x}}=x^{\frac12}-3x^{-\frac12}$$

   $$F(x)=\int \left(x^{\frac12}-3x^{-\frac12}\right)\,dx =\frac{x^{\frac32}}{\frac32}-3\cdot \frac{x^{\frac12}}{\frac12}+C =\frac23x^{\frac32}-6x^{\frac12}+C$$

Ответ

1) $$F(x)=\frac45x^{\frac52}+\frac23x^{\frac32}+C$$
2) $$F(x)=\frac97x^{\frac73}-\frac32x^{\frac43}+C$$
3) $$F(x)=\frac35x^{\frac53}+6x^{\frac23}+C$$
4) $$F(x)=\frac23x^{\frac32}-6x^{\frac12}+C$$