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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
How Do You Solve the Integral of 2 (x^2-1)dx? - Physics Forums The full question is to find the integral over infinity and 2, so i have to use limits I am getting an undefined answer since ln of infinity minus ln infinity is undefined does that sound right?
How can I solve integrals of the form x^n e^ (-x^2) by hand? Homework Statement Doing calculations for quantum mechanics, I have stumbled upon several integrals which I cannot solve by hand All of these have the form: \\int x^n exp[-x^2] dx For instance, when calculating the expectation value for x^2, the integral reduces to
Understanding the integral of 1 (1+x^2) • Physics Forums The integral of 1 (1+x^2) is indeed arctan(x), and no substitution is necessary to find this antiderivative since the derivative of arctan(x) is 1 (1+x^2) Substituting x with tan(Θ) transforms the integrand but can complicate the process unnecessarily, as the antiderivative is already known Understanding the substitution method is valuable, but it is essential to recognize that the goal is