$\int \frac{e^{3 x} + e^{5 x}}{e^{x} + e^{- x}} d x$

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Solution

According to question,

$\int \frac{e^{3 x} + e^{5 x}}{e^{x} + e^{- x}} d x$

$⟹ \int e^{4 x} \frac{(e^{x} + e^{- x})}{e^{x} + e^{- x}} d x$

$⟹ \int e^{4 x} d x$

$⟹ \frac{e^{4 x}}{4}$ +C

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Similar questions

\int \frac{e^{5 x} + e^{3 x}}{e^{x} + e^{- x}} d x =

\frac{e^{x} + e^{5 x}}{e^{3 x}} = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} . . . .

2 a_{1} + 2^{3} a_{3} + 2^{5} a_{5} + . . . .

\frac{e^{5 x} + e^{x}}{e^{3 x}}

x

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\int \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} d x

\int \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} d x

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