∫ s i n 3 x s e c 5 x dx equal to -

∫ ( s i n x ) 3/2 ( s e c x ) 5/2 dt = ∫ ( t a n x ) 3/2 s e c 4 xdx , tan x = t ∫ ( t 3/2 1 + t 2 ) d t = − 2 ( tan x 1 ) + 3 2 ( tan x ) 3/2 + C

Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationMiscellaneous formMedium2 minQB

MathematicsMediumsingle choice

$\int \frac{s e c ^{5} x}{s i n ^{3} x} dx$ equal to -

Answer:

Solution:

$\int \frac{( s e c x ) ^{5/2}}{( s i n x ) ^{3/2}} dt = \int \frac{s e c ^{4} xdx}{( t a n x ) ^{3/2}}, tan x = t$

$\int (\frac{1 + t ^{2}}{t ^{3/2}}) d t = - 2 (\frac{1}{tan x}) + \frac{2}{3} (tan x)^{3/2} + C$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Miscellaneous form

⏱ 2mℹ️ Source: QB

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