- #1

karush

Gold Member

MHB

- 3,269

- 5

Evaluate the integral.

$$\displaystyle \int_2^4

\dfrac{x+2}{x^2+3x-4}\, dx$$

W|A returned these partial fractions but I don't know where the the A=2 B=3 and 5 came from

$$

\dfrac{x+2}{(x+4)(x-1)}

=\dfrac{2}{5(x+4)}+\dfrac{3}{5(x-1)}$$

the book answer was

$$\dfrac{4}{5}\ln{2}+\dfrac{1}{5}\ln {3}

=\dfrac{1}{5}\ln{48}$$

$$\displaystyle \int_2^4

\dfrac{x+2}{x^2+3x-4}\, dx$$

W|A returned these partial fractions but I don't know where the the A=2 B=3 and 5 came from

$$

\dfrac{x+2}{(x+4)(x-1)}

=\dfrac{2}{5(x+4)}+\dfrac{3}{5(x-1)}$$

the book answer was

$$\dfrac{4}{5}\ln{2}+\dfrac{1}{5}\ln {3}

=\dfrac{1}{5}\ln{48}$$

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