Question

If $\int \frac{ dx }{\sqrt{ px + q }-\sqrt{ px + r }}=\frac{2}{3 k }\left[( px + q )^{\frac{3}{2}}+( px + r )^{\frac{3}{2}}\right]+ C , p \neq 0, q \neq r \neq p$, then $k$ is equal to

• A. $p (q - r)$
• B. $p(r-q)$
• C. $q(r-p)$
• D. $q(p-r)$

Answer 1

Answer: (A)

$\int \frac{\sqrt{p x+q}+\sqrt{p x+r}}{q-r} d x=\frac{1}{q-r} \int\left((p x+q)^{\frac{1}{2}}+(p x+r)^{\frac{1}{2}}\right) d x$
$=\left(\frac{1}{q-r}\right) \cdot \frac{2}{3 p}\left((p x+q)^{\frac{3}{2}}+(p x+r)^{\frac{3}{2}}\right)$