Evaluate the integral. \int_{2}^{3}[3x^{2}+2x+\frac{1}{x^{2}}]dx

Use a symbolic integration utility to find the indefinite integral.
${\displaystyle \int {(4t-3)}^{2}dt}$

Using the Euler's method (with $h={10}^{-n}$) to find $y(1)$
$y^{\prime }=\frac{\sin (x)}{x}$
Since
$y^{\prime }(x)=\frac{\sin (x)}{x}$
then
$f(x,y)=\frac{\sin (x)}{x}$
I know
$y_{n+1}=y_n+h\cdot f(x_n,y_n)$
and given $y(0)=0$, so
$x_0=y_0=0$
Therefore,
$x_1=x_0+h=0+{10}^{-0}=1\Rightarrow y_1=y(x_1)=y(1)$
Then,
$y_1=0+{10}^{-0}\cdot f(x_0,y_0)$
$y_1=f(0,0)$
But
$f(0,0)=\frac{\sin (0)}{0}=\frac{0}{0}$
How am I supposed to do it?

Why does the integral of $\frac{1}{\sqrt{a^2-x^2}}$ have 2 different answers for the same domain

Find the standard form of the equation of the circle having the following properties.
Center at the point (8,-6) Tangent to the x-axis
type the standard form of the equation of this circle

Use a change of variables to evaluate the following integral.
$\int -({\cos }^{7}x-5{\cos }^{5}x-\cos x)\sin xdx$

How can we use Euler's method to approximate the solutions for the following IVP below:
$y^{\prime }=-y+t{y}^{1/2},\text{ with }1\le t\le 2,y(1)=2,$
and with $h=0.5$
The main concern is the organization, i.e., set up of it for this particular example.

And, if the actual solution to the IVP above is:
$y(t)=(t-2+\sqrt{2}\mathrm{e}\cdot {\mathrm{e}}^{-t/2}{)}^2$
then, how to compare the actual error and compare the error bound?