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I have recently been playing with integrals and I still do not fully understand them.

Usually the best way for me to learn is to play with values and figure it out on my own, so I would like you (physics forum) to check my work so far.

After a bit of time I got this:

[tex]\int_{0}^{t}ax^ndx=\frac{at^{n+1}}{n+1}, n\neq-1[/tex]

and after figuring out:

[tex]\int_{0}^{t}ax+bxdx=\int_{0}^{t}axdx+\int_{0}^{t}bxdx[/tex]

I got this equation.

[tex]\int_{0}^{t}ax^n+bx^{n-1}+cx^{n-2} \cdots +ex dx=\int_{0}^{t}ax^ndx+\int_{0}^{t}bx^{n-1}dx+\int_{0}^{t}cx^{n-2}dx \cdots +\int_{0}^{t}(ex)dx=\frac{at^{n+1}}{n+1}+\frac{bt^n}{n}+\frac{ct^n-1} {n-1} \cdots +et[/tex]

Is this true for all polynomials (in standard form)? or does it even work at all?

Usually the best way for me to learn is to play with values and figure it out on my own, so I would like you (physics forum) to check my work so far.

After a bit of time I got this:

[tex]\int_{0}^{t}ax^ndx=\frac{at^{n+1}}{n+1}, n\neq-1[/tex]

and after figuring out:

[tex]\int_{0}^{t}ax+bxdx=\int_{0}^{t}axdx+\int_{0}^{t}bxdx[/tex]

I got this equation.

[tex]\int_{0}^{t}ax^n+bx^{n-1}+cx^{n-2} \cdots +ex dx=\int_{0}^{t}ax^ndx+\int_{0}^{t}bx^{n-1}dx+\int_{0}^{t}cx^{n-2}dx \cdots +\int_{0}^{t}(ex)dx=\frac{at^{n+1}}{n+1}+\frac{bt^n}{n}+\frac{ct^n-1} {n-1} \cdots +et[/tex]

Is this true for all polynomials (in standard form)? or does it even work at all?

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