Evaluate the following integrals- - e2xdx- x - R

The correct option is A e^2x2+c As we know that, ∫ a^xdx=a^xlna+c we can write, ∫ e^2xdx=∫(e^2)^xdx=(e^2)^xlne^2+c=e^2x2lne+c=e^2x2+c ...

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Integration by Substitution

Evaluate the ...

Question

Evaluate the following integrals:
$\int e^{2 x} d x$ , $x ϵ R$

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

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\frac{e^{2 x}}{2} + c

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\frac{e^{4 x}}{4} + c

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e^{2 x} + c

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{lim}_{x \to 0} \frac{e^{3 x} - e^{2 x}}{e^{4 x} - e^{3 x}}

\int \frac{e^{2 x}}{e^{4 x} - e^{2 x} + 2}

\int \frac{e^{3 x} + e^{x}}{e^{4 x} - e^{2 x} + 1} d x =

ln 4 \int 0 \frac{3 e^{4 x} + 2 e^{3 x} + e^{2 x} - 4}{e^{4 x} + e^{3 x} + e^{2 x} + e^{x} + 4} d x = ln (\frac{a}{4})

a \in R

a

ln 4 \int 0 \frac{3 e^{4 x} + 2 e^{3 x} + e^{2 x} - 4}{e^{4 x} + e^{3 x} + e^{2 x} + e^{x} + 4} d x = ln (\frac{a}{4})

a \in R

a

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