25. If /13 -a/10 - VB V5, then a = (b) -6 (c)-4

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t^{2} \int 0 x F (x) d x = \frac{2}{5} t^{5}

, then

F (\frac{4}{25}) =

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Let $$y=\sin^{-1}{(\sin{8})}-\tan^{-1}{(\tan{10})}+\cos^{-1}{(\cos{12})}-\sec^{-1}{(sec{9})}+\cot^{-1}{(\cot{6})}-cosec^{-1}{(cosec{7})}$$. If simplifies to $$a\pi+b$$, then find $$(a-b)$$.

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\int x^{\frac{13}{2}} . {(1 + x^{\frac{5}{2}})}^{\frac{1}{2}} d x = A {(1 + x^{\frac{5}{2}})}^{\frac{7}{2}} + B {(1 + x^{\frac{5}{2}})}^{\frac{5}{2}} + C {(1 + x^{\frac{5}{2}})}^{\frac{3}{2}}

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T_{n} = {sin}^{n} θ + {cos}^{n} θ

, then

\frac{_{3} - T_{5}}{T_{1}} \neq \frac{T_{5} - T_{7}}{T_{3}}

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T_{n} = {sin}^{n} x + {cos}^{n} x

, then find

\frac{T_{3} - T_{5}}{T_{1}} - \frac{T_{5} - T_{7}}{T_{3}}

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