Question

integral of 2x/xˆ2+1 dx is my solution right? ln(xˆ3+4x)+c ???

Answer 1

best way to find if the answer of the integral is right is taking the derivative of the answer and see if it is equal to the question.
So the question is,
\[\int \frac{2x}{x^2+1} dx\]

Answer you got -> \(\ln(x^3+4x)+c\)
taking the derivative,
\[\begin{align}
\frac{d [\ln(x^3+4x) +c]}{dx} &= \frac{3x^2+4}{x^3+4x}
\end{align}\]
which is not the same as the question

As a hint for getting the answer,
there is a property
\[\int \frac{y'}{y}dx = \ln(y) + c\] which kinda matches your question if you put \(y=x^2+1\)

Answer 2

THanx alot :) I have another Q. is the integer of x+8/(xˆ3+4x)dx = 2/6x.ln(xˆ3+4x)+c ??