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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Indefinite Integration

NTA Abhyas 2020 · Mathematics · Indefinite Integration

If I _ n = ∫ (ln x)ndx , then I _ 10 + 10 I _ 9 is equal to (where...

If

{I}_{n} = ∫ \left(ln x\right)ndx

, then

{I}_{10} + 10{I}_{9}

is equal to (where

C

& is the constant of integration)

Options

A $x\left(ln x\right)10+ C$
B $10{\left(ln x\right)}^{9}+ C$
C $9{\left(ln x\right)}^{10}+ C$
D $x\left(ln x\right)^{9}+ C$

Correct answer

A. $x\left(ln x\right)10+ C$

Step-by-step solution

{I}_{n} = ∫ \left(ln x\right)ndx

{I}_{n} = x\left(ln x\right)n - ∫ \dfrac{xn\left(ln x\right)n - 1}{x}dx

{Ι}_{n} = x\left(ln x\right)n - {nΙ}_{n - 1}

{I}_{n} + n{I}_{n - 1} = x\left(ln x\right)n + C

{I}_{10} + 10{I}_{9} = x\left(ln x\right)10+ C

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