Integrate the following with respect to the respective variable: x7x+1 - Mathematics and Statistics

प्रश्न

Integrate the following with respect to the respective variable:

$\frac{x^{7}}{x + 1}$

योग

उत्तर

Let I = $\int \frac{x^{7}}{x + 1} \cdot d x$

= $\int \frac{(x^{7} + 1) - 1}{x + 1} \cdot d x$

= $\int \frac{(x + 1) (x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1) - 1}{x + 1} \cdot d x$

= $\int [x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 - \frac{1}{x + 1}] \cdot d x$

= $\int x^{6} d x - \int x^{5} d x + \int x^{4} d x - \int x^{3} d x + \int x^{2} d x - \int x d x + \int 1 d x - \int \frac{1}{x + 1} d x$

= $\frac{x^{7}}{7} - \frac{x^{6}}{6} + \frac{x^{5}}{5} - \frac{x^{4}}{4} + \frac{x^{3}}{3} - \frac{x^{2}}{2} + x - \log | x + 1 | + c$ .

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Methods of Integration: Integration by Substitution

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 2.2 Q 2.1 Q 2.3

अध्याय 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १५०]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board

अध्याय 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 2.2 | पृष्ठ १५०

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Integrate the following with respect to the respective variable: x7x+1 - Mathematics and Statistics

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Integrate the following with respect to the respective variable: x7x+1 - Mathematics and Statistics

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