Question

Please vSolve the question

Answer 1

u can solve it by partial fraction

Answer 2

Answer:

-3log(x-1)+4log(x-2)+$\frac{-2x-1}{(x-2)^{2}}$

Step-by-step explanation:

We will solve using partial fraction method,

∫$\frac{x^{3}+2}{(x-2)^{3}(x-1)}$ =$\frac{A}{x-1} +\frac{B}{x-2} +\frac{C}{(x-2)^2}+\frac{D}{(x-2)^3}$

After solving, we get A = -3 B = 4 C=2 D = 10

So the integrand now becomes,

∫$\frac{-3}{x-1}$ +∫$\frac{4}{x-2}$ +∫$\frac{2}{(x-2)^2}$+∫$\frac{10}{(x-2)^3}$

-3log(x-1) +4log(x-2)-$\frac{2}{x-2}$+$\frac{-5}{(x-2)^{2}}$ [Using partial fraction in $\frac{10}{(x-2)^{3}}$]

Hence, the answer is:

-3log(x-1)+4log(x-2)+$\frac{-2x-1}{(x-2)^{2}}$