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∫ ( E X + 1 ) 2 E X D X - Mathematics

Sum

\[\int \left( e^x + 1 \right)^2 e^x dx\]

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Solution

\[\int \left( e^x + 1 \right)^2 e^x dx\]

\[ = \int\left( e^{2x} + 2 e^x + 1 \right) e^x dx\]

\[ = \int\left( e^{3x} + 2 e^{2x} + e^x \right) dx\]

\[ = \left[ \frac{e^{3x}}{3} + \frac{2 e^{2x}}{2} + e^x \right] + C\]

Concept: Indefinite Integral Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.3 | Q 14 | Page 23
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