Question
Asked Oct 29, 2019
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Evaluate the integral
6
dx
(x+1) (x2+4)
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Evaluate the integral 6 dx (x+1) (x2+4)

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Expert Answer

Step 1

Given,

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6 (x+1)(x +4)

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Step 2

Now

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1 Bx C Consider (x+1)(x +4) 1 A(x24)+(Bx C)(x +1) 1-Ax24A +Bx2 +Bx + Cx+C 1=(A B)x +(B+C)x +44C Equating the coefficients of x' , x and constant terms, we get A+B 0 B C 0 4A+C 1 1 and C On solving these equations, we get A = 5 В - 5

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Step 3

Therefore given inte...

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1 1 1 5 dx 5 5 . dx 6 x +1 (x+1)(x° +4) 1 dx 5 x +4 1 x -dx 5 x4 5 x 1 Put x4 tin the second integral dt 2x d dt x-d 2 6 1 - -dx 6 1 -dx 5 x2 1 (x+1)(x + 4) 5 t 5 x1 1 1 arctan =6 C 10 2

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Tagged in

Math

Calculus

Integration