Factor a 3 out of the denominator, and then use a trig substitution, which will involve a tangent.10martineze said:Hi everyone! I need to find the antiderivative(1/(3x^2 + 2)) but am not sure which approach to take. I have tried the following only to arrive at a dead end.
1/3x2+2= .5(1/(3(x/sqrt(2))2+1)= (1/6)(1/((x/sqrt(6))2+(1/3))
Thank you so much!
"Calc II integral with quadratic in numerator" refers to a type of integral that involves a quadratic expression in the numerator of the integrand. It is a topic commonly covered in a second semester Calculus course.
To solve a Calc II integral with quadratic in numerator, you can use various methods such as integration by parts, substitution, or partial fractions. The specific method used will depend on the form of the integral.
Yes, an example of a Calc II integral with quadratic in numerator is ∫(x^2 + 3x + 2)/(x^2 + 4x + 3) dx. This integral can be solved using partial fractions and results in the final answer of ln(x+1) + 2ln(x+3) + C.
A quadratic in the numerator of an integral signifies that the function being integrated is not a simple polynomial, and therefore requires more advanced techniques to solve. It also often indicates that the integral will result in logarithmic or arctangent functions in the final answer.
A Calc II integral with quadratic in numerator can be used in real life to model various physical phenomena, such as the motion of a falling object or the rate of change of a population. It can also be used in engineering and economics to calculate areas, volumes, and other quantities.