# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\:\frac{-x^2+8x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{7x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of (-x^2+8x^2-9x+2)/((x^2+1)(x-3)^2) with respect to x. Adding -1x^2 and 8x^2. Rewrite the fraction \frac{7x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by \left(x^2+1\right)\left(x-3\right)^2. Multiplying polynomials.

$-\frac{51}{100}\ln\left(x^2+1\right)+\frac{7}{50}\arctan\left(x\right)+\frac{-\frac{19}{5}}{x-3}+\frac{51}{50}\ln\left|x-3\right|+C_0$

### Problem Analysis

$\int\:\frac{-x^2+8x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

### Main topic:

Integrals by partial fraction expansion

~ 0.28 seconds