<s>[INST] Evaluation of $\int x^{26}(x-1)^{17}(5x-3)dx$ 
Evaluation of $$\int x^{26}(x-1)^{17}(5x-3) \, dx$$

I did not understand what substution i have used so that it can simplify,
I have seems it is a derivative of some function.
Help me, Thanks 
 [/INST] Sorry for the informal writing am rushing out.
Hope it helps!
$$
(x - 1)^{17} = \sum \left(
    \begin{array}{c}
      17 \\
      r
    \end{array}
  \right) x^{17-r}(-1)^r
\\
x^{26}(x - 1)^{17} = \sum \left(
    \begin{array}{c}
      17 \\
      r
    \end{array}
  \right) x^{43-r}(-1)^r
\\
 x^{26}(x - 1)^{17}(5x−3) = 5\sum \left(
    \begin{array}{c}
      17 \\
      r
    \end{array}
  \right) x^{45-r}(-1)^r\space- 3\sum\left(
    \begin{array}{c}
      17 \\
      r
    \end{array}
    \right) x^{44-r}(-1)^r
\\
=5x^{45} - \left(\sum\left[
                     5\left( \begin{array}{c}
      17 \\
      r+1
    \end{array}\right) - 3\left( \begin{array}{c}
      17 \\
      r
    \end{array}\right)
               \right]x^{44-r}(-1)^r\right)
+3x^{27}
\\
\int x^{26}(x - 1)^{17}(5x−3) = 5\int x^{45} - \left(\sum\left[
                     5\left( \begin{array}{c}
      17 \\
      r+1
    \end{array}\right) - 3\left( \begin{array}{c}
      17 \\
      r
    \end{array}\right)
               \right]\int x^{44-r}(-1)^r\right)
\\+3\int x^{27} + c
$$
</s>