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What is the Integral of 2^(x)? - Physics Forums The integral of 2^x can be solved using the relationship between derivatives and integrals The derivative of 2^x is ln(2) * 2^x, which leads to the conclusion that the anti-derivative is (1 ln(2)) * 2^x
What is the Integral of -e^(-x)? • Physics Forums The integral of -e^(-x) is derived using u-substitution, where u = -x, leading to the result -e^(-x) + C The negative sign arises because the derivative of -x is -1, thus requiring division by -1 during integration The discussion emphasizes that integration can be viewed as the reverse of differentiation, which simplifies the process
Integrate exp(-x^2), dx • Physics Forums This integral can be done the same way that the integral of exp(-x2) can be done First, write the integral of x2exp(-x2) from zero to infinity Then write the integral of y2exp(-y2) from zero to infinity (they're both exactly the same as your integral) Now multiply the integrands together double integrate over x and y When you convert to polar coordinates, you will get an integral that can