Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)1 Mark
Question
Evalute : $\int(x+1)(x+2)^7(x+3) d x$
✓
Answer
$ \begin{aligned} & \text { Let I }=\int(x+1)(x+2)^7(x+3) d x \\ & =\int(x+2)^7(x+1)(x+3) d x \\ & =\int(x+2)^7[(x+2)-1][(x+2)+1] d x \\ & =\int(x+2)^7\left[(x+2)^2-1\right] d x \\ & =\int\left[(x+2)^9-(x+2)^7\right] d x \\ & =\int(x+2)^9 d x-\int(x+2)^7 d x \\ & =\frac{(x+2)^{10}}{10}-\frac{(x+2)^8}{8}+c \end{aligned} $
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