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What will be the integration of the following wrt x?

$\int_{0}^{x} x {(1 + x)}^{n}$

D e a r s t u d e n t I = \int_{0}^{x} x {(1 + x)}^{n} d x L e t 1 + x = t x = t - 1 d t = d x I = \int_{1}^{x + 1} (t - 1) t^{n} d t = \int_{1}^{x + 1} t^{n + 1} d t - \int_{1}^{x + 1} t^{n} d t I = {[\frac{t^{n + 2}}{n + 2}]}_{1}^{x + 1} - {[\frac{t^{n + 1}}{n + 1}]}_{1}^{x + 1} = \frac{{(x + 1)}^{n + 2}}{n + 2} - \frac{1}{n + 2} - \frac{{(x + 1)}^{n + 1}}{n + 1} + \frac{1}{n + 1} = \frac{{(x + 1)}^{n + 2}}{n + 2} - \frac{{(x + 1)}^{n + 1}}{n + 1} + \frac{1}{(n + 1) (n + 1)}

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