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lost_2
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HI there! i was wondering if you could help me with this..
how do you integrate -2xy/(1+x^2)?
Thank you.
how do you integrate -2xy/(1+x^2)?
Thank you.
Welcome to the forums,lost_2 said:HI there! i was wondering if you could help me with this..
how do you integrate -2xy/(1+x^2)?
Thank you.
Thanks, it's always a good idea to post the entire question. So you know that,lost_2 said:Anyways this is the whole qns.
find the equation of the curve in the xy plane that passes through (1,2) and whose tangent line at a point (x,y) has a slope of -2xy/(1+x^2).
Integrating refers to the process of finding the antiderivative of a given function. Essentially, it involves finding a function whose derivative is equal to the given function.
The notation -2xy/(1+x^2) represents a function that includes variables x and y and is divided by the expression 1+x^2. This type of function is known as a rational function.
To solve for the antiderivative, we use the rules of integration, which include power rule, product rule, and chain rule. We also use the techniques of substitution and integration by parts to simplify the function and find its antiderivative.
First, we split the rational function into two separate fractions: -2xy and 1/(1+x^2). Next, we use the substitution technique by assigning u = 1+x^2 to the second fraction. Then, we apply the power rule and product rule to find the antiderivative of each fraction. Finally, we substitute back the value of u and simplify the expression to get the final solution.
The final solution is given by: -xy - ln|1+x^2| + C, where C is the constant of integration. This solution can also be written as -xy - ln(1+x^2) + C, where ln represents the natural logarithm function.