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Grade 12Differential Calculus

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milind

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Hello student,
Please find answer to your question
$I_{n} = \frac{d^{n}}{dx^{n}}(x^{n}log(x))$
$I_{1} = \frac{d^{1}}{dx^{1}}(x^{1}log(x))$
$I_{1} =1 + log(x)$
$I_{2} = \frac{d^{2}}{dx^{2}}(x^{2}log(x))$
$I_{2} = 3 + 2log(x)$
$I_{3} = \frac{d^{3}}{dx^{3}}(x^{3}log(x))$
$I_{3} = 11 + 6log(x)$
$I_{4} = \frac{d^{4}}{dx^{4}}(x^{4}log(x))$
$I_{4} =50 + 24log(x)$
$I_{5} = \frac{d^{5}}{dx^{5}}(x^{5}log(x))$
$I_{5} = 274 + 120log(x)$
$I_{5}-5I_{4} = 24 = 4! = (5-1)!$
$I_{4}-4I_{3} = 6 = 3! = (4-1)!$
$I_{3}-3I_{2} = 2 = 2! = (3-1)!$
$I_{2}-2I_{1} = 1 = 1! = (2-1)!$
Similarly for n,
$I_{n} = A + n!log(x)$
$I_{n-1} = B + (n-1)!log(x)$
$I_{n}-nI_{n-1} = A - nB = (n-1)!$

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