Use a table of integrals to evaluate the following integrals. $$\int {x}^{2}{e}^{5x}dx$$

daniko883y
2022-10-01
Answered

Use a table of integrals to evaluate the following integrals. $$\int {x}^{2}{e}^{5x}dx$$

You can still ask an expert for help

Garrett Valenzuela

Answered 2022-10-02
Author has **9** answers

From the Table of Integrals:

$$\int {x}^{2}{e}^{ax}dx=(\frac{{x}^{2}}{a}-\frac{2x}{{a}^{2}}+\frac{2}{{a}^{3}}){e}^{ax}+C$$

Therefore:

$$\int {x}^{2}{e}^{5x}dx=(\frac{{x}^{2}}{5}-\frac{2x}{25}+\frac{2}{125}){e}^{5x}+C$$

Result:

$$(\frac{{x}^{2}}{5}-\frac{2x}{25}+\frac{2}{125}){e}^{5x}+C$$

$$\int {x}^{2}{e}^{ax}dx=(\frac{{x}^{2}}{a}-\frac{2x}{{a}^{2}}+\frac{2}{{a}^{3}}){e}^{ax}+C$$

Therefore:

$$\int {x}^{2}{e}^{5x}dx=(\frac{{x}^{2}}{5}-\frac{2x}{25}+\frac{2}{125}){e}^{5x}+C$$

Result:

$$(\frac{{x}^{2}}{5}-\frac{2x}{25}+\frac{2}{125}){e}^{5x}+C$$

asked 2021-12-12

Evaluate the indefinite integral.

$\int \frac{{e}^{t}dt}{{e}^{2t}+2{e}^{t}+1}$

asked 2021-12-29

Evaluate the integrals.

$\int x{\mathrm{sin}x}^{2}{\mathrm{cos}}^{8}{x}^{2}dx$

asked 2022-04-11

How do you solve for xy'-y=3xy given y(1)=0?

asked 2022-07-02

Trying to integrate

$\int \mathrm{cos}(z)\mathrm{d}z$

where z is a complex number. What is a good way to do so?

$\int \mathrm{cos}(z)\mathrm{d}z$

where z is a complex number. What is a good way to do so?

asked 2022-07-07

Investigate to relationship $\int {\displaystyle \frac{-2\mathrm{cos}xdx}{(1-\mathrm{sin}x{)}^{2}}}$ shares with $({\displaystyle \frac{1+\mathrm{sin}x}{1-\mathrm{sin}x}})$I have used integration by recognition to go about it showing that,

$\frac{d}{dx}}({\displaystyle \frac{1+\mathrm{sin}x}{1-\mathrm{sin}x}})={\displaystyle \frac{-2\mathrm{cos}x}{(1-\mathrm{sin}x{)}^{2}}$

However, when I tried integrating $\frac{-2cosx}{(1-sinx{)}^{2}}$ I don't arrive back at $\frac{1+sinx}{1-sinx}$

So, how do you integrate $\frac{-2\mathrm{cos}x}{(1-\mathrm{sin}x{)}^{2}}$?

$\frac{d}{dx}}({\displaystyle \frac{1+\mathrm{sin}x}{1-\mathrm{sin}x}})={\displaystyle \frac{-2\mathrm{cos}x}{(1-\mathrm{sin}x{)}^{2}}$

However, when I tried integrating $\frac{-2cosx}{(1-sinx{)}^{2}}$ I don't arrive back at $\frac{1+sinx}{1-sinx}$

So, how do you integrate $\frac{-2\mathrm{cos}x}{(1-\mathrm{sin}x{)}^{2}}$?

asked 2022-05-20

What is the arc length of $f(x)=x\mathrm{sin}x-{\mathrm{cos}}^{2}x$ on $x\in [0,\pi ]$?

asked 2022-06-22

If R is the area enclosed by f(x) and g(x), is the volume of the solid generated by revolving R around the x-axis then revolving that solid around the y-axis equal to the volume of the solid generated if the order of the revolutions was switched?