Evaluate
\frac{4tx+3t}{2x^{2}+2x+1}+С
Differentiate w.r.t. x
-\frac{t\left(\left(4x+3\right)^{2}-5\right)}{2\left(2x^{2}+2x+1\right)^{2}}
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\frac{4x+3}{2x^{2}+2x+1}t
Find the integral of \frac{4x+3}{2x^{2}+2x+1} using the table of common integrals rule \int a\mathrm{d}t=at.
\frac{\left(4x+3\right)t}{2x^{2}+2x+1}
Simplify.
\frac{\left(4x+3\right)t}{2x^{2}+2x+1}+С
If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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