If ∫ ( 1 + x 2 ) 10 x 17 d x = n 1 ( 1 + x 2 x 2 ) m + C , where m , n ∈ N , find n / m in lowest form.

Put t = 1 + x 2 , then y = 1 − 1/ t = x 2 / ( 1 + x 2 ) . The integral becomes 2 1 ∫ y 8 d y = 18 1 y 9 + C . Thus m = 9 , n = 18 , and n / m = 2.00 .

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Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationMiscellaneous/MixedHard2 minQB

MathematicsHardnumerical

If $\int \frac{x ^{17}}{( 1 + x ^{2} ) ^{10}} d x = \frac{1}{n} (\frac{x ^{2}}{1 + x ^{2}})^{m} + C$ , where $m, n \in N$ , find $n / m$ in lowest form.

Answer:

2.00

Solution:

Put $t = 1 + x^{2}$ , then $y = 1 - 1/ t = x^{2} / (1 + x^{2})$ . The integral becomes $\frac{1}{2} \int y^{8} d y = \frac{1}{18} y^{9} + C$ . Thus $m = 9, n = 18$ , and $n / m = 2.00$ .

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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