$$\LARGE \int {(x + 1){{({x^2\;+}2x + 3)}^3}\,\,dx} $$

$$\LARGE \text{ATEMPTED}$$ (I followed wolframalpha's steps too ...):

$$\LARGE u=x^2+2x+3$$
and

$$\LARGE du=u'\;dx$$

$$\LARGE du=(x^2+2x+3)'\;dx$$

$$\LARGE du=2x+2\;dx$$

now (wolframa) when substitutes it goes like:

$$\LARGE \frac12 \;\int\limits u^2 \;du$$

But I'm extremely confused ... !!

Please show me steps too...

Question

$$\LARGE \int {(x + 1){{({x^2\;+}2x + 3)}^3}\,\,dx} $$

$$\LARGE \text{ATEMPTED}$$ (I followed wolframalpha's steps too ...):

$$\LARGE u=x^2+2x+3$$
and 

$$\LARGE du=u'\;dx$$

$$\LARGE du=(x^2+2x+3)'\;dx$$

$$\LARGE du=2x+2\;dx$$

now  (wolframa) when substitutes it goes like:

$$\LARGE \frac12 \;\int\limits u^2 \;du$$

But I'm extremely confused ... !!  

Please show me steps too...

mimi_x3 · Answer

$$\int\limits(x+1)u^{3}*\frac{du}{2x+2}   =>\int\limits(x+1)u^{3}*\frac{du}{2(x+1)}   =>\frac{1}{2}  \int\limits u^{3}  du$$

anonymous · Answer

Thank you very much, 100% got it  ;) @Mimi_x3

mimi_x3 · Answer

yw (: