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