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∫ 1 − X 4 1 − X Dx - Mathematics

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Sum

\[\int\frac{1 - x^4}{1 - x} \text{ dx }\]

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Solution

\[\int\left( \frac{1 - x^4}{1 - x} \right)dx\]
\[ = \int\frac{\left( 1 - x^2 \right) \left( 1 + x^2 \right)}{\left( 1 - x \right)}dx\]
\[ = \int\frac{\left( 1 - x \right) \left( 1 + x \right) \left( 1 + x^2 \right)}{\left( 1 - x \right)}dx\]
\[ = \int\left( 1 + x \right) \left( 1 + x^2 \right)dx\]
\[ = \int\left( 1 + x^2 + x + x^3 \right)dx\]
\[ = x + \frac{x^3}{3} + \frac{x^2}{2} + \frac{x^4}{4} + C\]

Concept: Indefinite Integral Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Revision Excercise | Q 2 | Page 203

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