Evaluate
\frac{\sqrt{1-x}t}{x^{\frac{3}{2}}}+С
Differentiate w.r.t. x
\frac{t\left(2x-3\right)}{2\sqrt{1-x}x^{\frac{5}{2}}}
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\frac{\sqrt{1-x}}{x^{\frac{3}{2}}}t
Find the integral of \frac{\sqrt{1-x}}{x^{\frac{3}{2}}} using the table of common integrals rule \int a\mathrm{d}t=at.
\frac{\sqrt{1-x}t}{x^{\frac{3}{2}}}
Simplify.
\frac{\sqrt{1-x}t}{x^{\frac{3}{2}}}+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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