#160; #160; #160; #160; #160; #160; #8747;ex+12ex #160;dx= #8747;e2x+2ex+1ex #160;dx= #8747;e3x+2e2x+ex #160;dx= #160;e3x3+2e2x2+ex+C ...

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Summation of Determinant

∫ e x+12 e x ...

Question

$\int {(e^{x} + 1)}^{2} e^{x} d x$

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Solution

$\int {(e^{x} + 1)}^{2} e^{x} d x = \int (e^{2 x} + 2 e^{x} + 1) e^{x} d x = \int (e^{3 x} + 2 e^{2 x} + e^{x}) d x = [\frac{e^{3 x}}{3} + \frac{2 e^{2 x}}{2} + e^{x}] + C$

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