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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 33 Maths Textbbok Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise  Revision Exercise Question 33 Maths Textbbok Solution.

Answers (1)

Answer:

\log |x-1|-\frac{2}{(x-1)}-\frac{1}{2(x-1)^{2}}+c

Given:

\int \frac{x^{2}}{(x-1)^{3}} d x

Hint:

To solve the statement we will use partial fractions

Solution:

Let \frac{x^{2}}{(x-1)^{3}} d x=\frac{A}{(x-1)}+\frac{B}{(x-1)^{2}}+\frac{C}{(x-1)^{3}}

x^{2}=A(x-1)^{2}+B(x-1)+c

x^{2}=x^{2} A+x(2 A+B)+A+B+C

On equating the coeffiecients of x^{2}: A=1

On equating the coeffiecients of x: B=-2

On equating the constants :C=1

Thus,\int \frac{x^{2}}{(x-1)^{3}} d x=\int \frac{1}{(x-1)} d x+\int \frac{-2}{(x-1)^{2}} d x+\int \frac{1}{(x-1)^{3}} d x

 

=\log |x-1|+\frac{2(x-1)^{-2+1}}{-2+1}-\frac{1}{2(x-1)^{2}}+c

=\log |x-1|-\frac{2}{(x-1)}-\frac{1}{2(x-1)^{2}}+c

 

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