Question
Evaluate the following integrals
a) .
b) .
Answer :
Word Count : 92
Consider first [ I_1=\int_{0}^{\infty}\frac{x^{2}+2}{(x^{2}+1)(x^{2}+4)},dx . ] Decompose the integrand into partial fractions: [ \frac{x^{2}+2}{(x^{2}+1)(x^{2}+4)}=\frac{A}{x^{2}+1}+\frac{B}{x^{2}+4}. ] Thus [ x^{2}+2=A(x^{2}+4)+B(x^{2}+1)=(A+B)x^{2}+(4A+B). ] Equating coefficients gives [ _____ _________ ____ ___ ___ _________ _________ ________ __________ _____ _______ _________.
_____ ______ ___ _________ _____.
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_________ ______ ______ ________ __________ ____ _________ __________ ________ ____ ________.
______ __________ ________ ______ ______ ______ __________ ______ _______.
______ _________ ______ ________ ______ ______ ____.
_______ ___ ______ _________ __________.
____ ______ ______ ________.
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Consider first [ I_1=\int_{0}^{\infty}\frac{x^{2}+2}{(x^{2}+1)(x^{2}+4)},dx . ] Decompose the integrand into partial fractions: [ \frac{x^{2}+2}{(x^{2}+1)(x^{2}+4)}=\frac{A}{x^{2}+1}+\frac{B}{x^{2}+4}. ] Thus [ x^{2}+2=A(x^{2}+4)+B(x^{2}+1)=(A+B)x^{2}+(4A+B). ] Equating coefficients gives [ _____ _________ ____ ___ ___ _________ _________ ________ __________ _____ _______ _________.
_____ ______ ___ _________ _____.
________ ________ ____ ____ _____ ___ ______ ________ _____ _________ _____.
_____ __________ ___ ___ ___.
_________ ______ ______ ________ __________ ____ _________ __________ ________ ____ ________.
______ __________ ________ ______ ______ ______ __________ ______ _______.
______ _________ ______ ________ ______ ______ ____.
_______ ___ ______ _________ __________.
____ ______ ______ ________.
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