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Created on: 2011-12-07

A sample problem solved by Quickmath web algebra solver

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Expression

2*%pi*((-4)*G^2*M^2*log(2*abs(G)*abs(M))/c^4+4*G^2*M^2*log(2*G*M+c^2*r)/c^4+(-2)*r*G*M/c^2+r^2/2)

  1. A product consisting of 3 factors; the first factor of the product is two; the second factor of the product is equal to; pi; the third factor of the product is equal to a sum comprising 4 terms; the first term of the sum is a fraction: the numerator of the fraction is a product of 4 factors; the first factor of the product is equal to negative four; the second factor of the product is a power; the base is G; the exponent is two; the third factor of the product is a power; the base is M; the exponent is two; the four factor of the product is logarithm of a product of 3 factors; the first factor of the product is equal to two; the second factor of the product is absolute value of G; the third factor of the product is equal to absolute value of M; the denominator of the fraction is a power; the base is c; the exponent is four; the second term of the sum is a fraction: the top of the fraction is a product consisting of 4 factors; the first factor of the product is equal to four; the second factor of the product is equal to a power; the base is G; the exponent is two; the third factor of the product is a power; the base is M; the exponent is two; the four factor of the product is logarithm of a sum that comprises 2 terms; the first term of the sum is a product that contains 3 factors; the first factor of the product is two; the second factor of the product is equal to G; the third factor of the product is M; the second term of the sum is equal to a product that comprises 2 factors; the first factor of the product is equal to a power; the base is c; the exponent is two; the second factor of the product is r; the bottom of the fraction is a power; the base is c; the exponent is four; the third term of the sum is equal to a fraction: the numerator of the fraction is a product of 4 factors; the first factor of the product is equal to negative two; the second factor of the product is equal to r; the third factor of the product is equal to G; the four factor of the product is equal to M; the denominator of the fraction is a power; the base is c; the exponent is two; the four term of the sum is equal to a quotient: dividend of the quotient is a power; the base is r; the exponent is two; divisor of the quotient is two;
  2. two times; pi multiplied by open parenthesis left brace negative four right brace times G exponentiated by two times M raised to the power two times logarithm of two multiplied by absolute value of G times absolute value of M fraction line c to the power four plus four multiplied by G exponentiated by two multiplied by M raised to the power of two multiplied by logarithm of two multiplied by G multiplied by M plus c exponentiated by two times r fraction line c to the power of four plus open brace negative two close brace multiplied by r multiplied by G times M over c to the power of two plus r to the power of two fraction line two close parenthesis;

Result

-(8*%pi*G^2*M^2*log(2*abs(G)*abs(M))-8*%pi*G^2*M^2*log(2*G*M+c^2*r)+4*%pi*c^2*r*G*M-%pi*c^4*r^2)/c^4

  1. A fraction: the top of the fraction is a negative sum consisting of 4 terms. The first term of the sum is a product that comprises 5 factors. The first factor of the product is equal to eight. The second factor of the product is equal to. Pi. The third factor of the product is a power . The base is G. The exponent is two. The four factor of the product is a power. The base is M. The exponent is two. The five factor of the product is equal to log of a product that contains 3 factors. The first factor of the product is equal to two. The second factor of the product is equal to absolute value of G. The third factor of the product is equal to absolute value of M. The second term of the sum is a negative product that comprises 5 factors. The first factor of the product is eight. The second factor of the product is equal to. Pi. The third factor of the product is equal to a power. The base is G. The exponent is two. The four factor of the product is a power. The base is M. The exponent is two. The five factor of the product is equal to logarithm of a sum containing 2 terms. The first term of the sum is equal to a product comprising 3 factors. The first factor of the product is equal to two. The second factor of the product is G. The third factor of the product is M. The second term of the sum is a product consisting of 2 factors. The first factor of the product is a power. The base is c. The exponent is two. The second factor of the product is equal to r. The third term of the sum is equal to a product containing 6 factors. The first factor of the product is four. The second factor of the product is equal to. Pi. The third factor of the product is equal to a power. The base is c. The exponent is two. The four factor of the product is r. The five factor of the product is equal to G. The six factor of the product is equal to M. The four term of the sum is equal to a negative product containing 3 factors. The first factor of the product is equal to. Pi. The second factor of the product is a power. The base is c. The exponent is four. The third factor of the product is a power. The base is r. The exponent is two. The bottom of the fraction is a power. The base is c. The exponent is four.
  2. negative open brace eight times. Pi multiplied by G to the power two times M raised to the power of two multiplied by logarithm of two multiplied by absolute value of G times absolute value of M plus negative eight multiplied by. Pi times G raised to the power of two times M exponentiated by two times logarithm of two times G times M plus c to the power two times r plus four multiplied by. Pi times c to the power two times r times G times M plus negative. Pi multiplied by c exponentiated by four times r to the power of two close brace over c to the power of four.