Question

determine the integral \int x^3+2x^2+x-1 dx

Answer 1

Answer:

$\displaystyle \longrightarrow \frac{x^4}{4} + \frac{2x^3}{3} + \frac{x^2}{2} - x +C$

Step-by-step explanation:

Let :

$\displaystyle \text{I}=\int\limits {(x^3+2x^2+x-1)} \, dx$

$\displaystyle \longrightarrow \text{I}=\int\limits {x^3 \, dx+\int\limits 2x^2 \, dx+\int\limits x \, dx-\int\limits 1} \, dx$

$\displaystyle \longrightarrow \text{I}= \frac{x^4}{4} + \frac{2x^3}{3} + \frac{x^2}{2} - \frac{x}{1} +C$

$\displaystyle \longrightarrow \text{I}= \frac{x^4}{4} + \frac{2x^3}{3} + \frac{x^2}{2} - x +C$

Hence we get required answer!

Read more :

√x+√y=√10 dy/dx find the derivative of the function

https://brainly.in/question/18397937

Answer 2

$Answer: \\ </p><p></p><p>\begin{gathered}\displaystyle \longrightarrow \frac{x^4}{4} + \frac{2x^3}{3} + \frac{x^2}{2} - x +C \\\end{gathered}⟶4x4+32x3+2x2−x+C</p><p></p><p>Step-by-step explanation: \\ </p><p></p><p>Let : \\ </p><p></p><p>\begin{gathered}\displaystyle \text{I}=\int\limits {(x^3+2x^2+x-1)} \, dx \\ \\\end{gathered}I=∫(x3+2x2+x−1)dx \\ </p><p></p><p>\begin{gathered}\displaystyle \longrightarrow \text{I}=\int\limits {x^3 \, dx+\int\limits 2x^2 \, dx+\int\limits x \, dx-\int\limits 1} \, dx \\ \\\end{gathered}⟶I=∫x3dx+∫2x2dx+∫xdx−∫1dx \\ </p><p></p><p>\begin{gathered}\displaystyle \longrightarrow \text{I}= \frac{x^4}{4} + \frac{2x^3}{3} + \frac{x^2}{2} - \frac{x}{1} +C \\ \\\end{gathered}⟶I=4x4+32x3+2x2−1x+C \\ </p><p></p><p>\begin{gathered}\displaystyle \longrightarrow \text{I}= \frac{x^4}{4} + \frac{2x^3}{3} + \frac{x^2}{2} - x +C \\ \\\end{gathered}⟶I=4x4+32x3+2x2−x+C \\ </p><p></p><p>Hence we get required answer! \\ </p><p></p><p>Read more : \\ </p><p></p><p>√x+√y=√10 dy/dx find the derivative of the function \\ </p><p></p><p>https://brainly.in/question/18397937</p><p></p><p>$