9. $$ \int\left(5-x^{3}+x\right) d x= $$ 10. $$ \int\left(x^{2}+2 \sqrt{x}\right) d x= $$

Question

UpStudy AI · Accepted Answer

Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int \left(5-x^{3}+x\right) dx$$
- step1: Use properties of integrals:
  $$\int 5 dx+\int -x^{3} dx+\int x dx$$
- step2: Evaluate the integral:
  $$5x+\int -x^{3} dx+\int x dx$$
- step3: Evaluate the integral:
  $$5x-\frac{x^{4}}{4}+\int x dx$$
- step4: Evaluate the integral:
  $$5x-\frac{x^{4}}{4}+\frac{x^{2}}{2}$$
- step5: Add the constant of integral C:
  $$5x-\frac{x^{4}}{4}+\frac{x^{2}}{2} + C, C \in \mathbb{R}$$
Calculate the integral $$ x^{2}+2 \sqrt{x} $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int \left(x^{2}+2\sqrt{x}\right) dx$$
- step1: Use properties of integrals:
  $$\int x^{2} dx+\int 2\sqrt{x} dx$$
- step2: Evaluate the integral:
  $$\frac{x^{3}}{3}+\int 2\sqrt{x} dx$$
- step3: Evaluate the integral:
  $$\frac{x^{3}}{3}+\frac{4}{3}x^{\frac{3}{2}}$$
- step4: Simplify:
  $$\frac{x^{3}}{3}+\frac{4}{3}x\sqrt{x}$$
- step5: Add the constant of integral C:
  $$\frac{x^{3}}{3}+\frac{4}{3}x\sqrt{x} + C, C \in \mathbb{R}$$
Aquí están las soluciones a las integrales solicitadas:

9. Para la integral $$ \int\left(5-x^{3}+x\right) d x $$:
   $$
   \int\left(5-x^{3}+x\right) d x = 5x - \frac{x^{4}}{4} + \frac{x^{2}}{2} + C, \quad C \in \mathbb{R}
   $$

10. Para la integral $$ \int\left(x^{2}+2 \sqrt{x}\right) d x $$:
   $$
   \int\left(x^{2}+2 \sqrt{x}\right) d x = \frac{x^{3}}{3} + \frac{4}{3}x\sqrt{x} + C, \quad C \in \mathbb{R}
   $$

Si necesitas más ayuda o aclaraciones, no dudes en preguntar.
9. $$ \int\left(5 - x^{3} + x\right) dx = 5x - \frac{x^{4}}{4} + \frac{x^{2}}{2} + C $$ 10. $$ \int\left(x^{2} + 2 \sqrt{x}\right) dx = \frac{x^{3}}{3} + \frac{4}{3}x\sqrt{x} + C $$

9. \( \int\left(5-x^{3}+x\right) d x= \) 10. \( \int\left(x^{2}+2 \sqrt{x}\right) d x= \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Calculus Questions