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# Evaluate the integrals in Exercises 1 to 8 using substitution. dx/ (x^2+2x+5)

Evaluate the integrals in Exercises 1 to 8 using substitution.

Q7.    $\int_{-1}^1\frac{dx}{x^2 +2x + 5}$

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$\int_{-1}^1\frac{dx}{x^2 +2x + 5}$
the Dr can be written as $x^2+2x+5 = (x+1)^2+2^2$
and put x+1 = t then dx =dt

when x= -1 then t = 0 and when x = 1 then t = 2

$\\\Rightarrow \int_{0}^{2}\frac{dt}{t^2+2^2}\\ =\frac{1}{2}[\tan^{-1}\frac{t}{2}]^2_0\\ =\frac{1}{2}( \pi/4)\\ =\frac{\pi}{8}$

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