The value of - e2x2sin 3x-3cos 3xdx is

The correct option is D e^2xsin 3x+c ∫ e^2x(2 sin 3x+3 cos 3x)dx it is in the form of ∫ e^x [ f(x)+f^'(x) ]dx =e^xf(x)+c so, ∫ e^2x(2 ...

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Byju's Answer

Standard XII

Mathematics

Property 7

The value of ...

Question

The value of $\int e^{2 x} (2 sin 3 x + 3 cos 3 x) d x$ is

e^{2 x} sin 3 x + c

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e^{2 x} cos 3 x + c

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e^{2 x} + c

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e^{2 x} (2 sin 3 x) + c

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Solution

The correct option is D $e^{2 x} sin 3 x + c$
$\int e^{2 x} (2 s i n 3 x + 3 c o s 3 x) d x$
it is in the form of
$\int e^{x} [f (x) + f^{^{'}} (x)] d x$
$= e^{x} f (x) + c$
$s o, \int e^{2 x} (2 s i n 3 x + 3 c o s 3 x) d x$
$= \int d (e^{2 x} s i n 3 x)$
$e^{2 x} s i n 3 x + c$
$s o, \int e^{2 x} (2 s i n 3 x + 3 c o s 3 x) d x$
$e^{2 x} s i n 3 x + c$

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Similar questions

Let I $= \int \frac{e^{x}}{e^{4 x} + e^{2 x} + 1} d x . J = \int \frac{e^{- x}}{e^{- 4 x} + e^{- 2 x} + 1} d x,$ Then, for an arbitrary constant c, the value of J-I equals

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

_____

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Q. If

\int \frac{x d x}{\sqrt{e^{2 x} - (x + 1)^{2}}} = {cos}^{- 1} (f (x)) + C,

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The value of ∫e2x(2sin3x+3cos3x)dx is

The correct option is D e2xsin3x+c∫e2x(2 sin 3x+3 cos 3x)dxit is in the form of∫ex[f(x)+f′(x)]dx=exf(x)+cso, ∫e2x(2 sin 3x+3 cos 3x)dx=∫d(e2xsin3x)e2xsin 3x+cso,∫e2x(2 sin 3x+3cos 3x)dxe2xsin 3x+c

The value of $\int e^{2 x} (2 sin 3 x + 3 cos 3 x) d x$ is