What is the integral of 49e^{-7x}sin(7x) ?

The integral of 49e^{-7x}sin(7x) is 49(-(e^{-7x}cos(7x))/(14)-(e^{-7x}sin(7x))/(14))+C

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integral of 49e^{-7x}sin(7x)

\int 49 e^{- 7 x} sin (7 x) d x

49 (- \frac{e ^{- 7 x} cos ( 7 x )}{14} - \frac{e ^{- 7 x} sin ( 7 x )}{14}) + C

Solution steps

\int 49 e^{- 7 x} sin (7 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 49 \cdot \int e^{- 7 x} sin (7 x) d x

Apply Integration By Parts

: - \frac{1}{7} e^{- 7 x} cos (7 x) - \int e^{- 7 x} cos (7 x) d x

= 49 (- \frac{1}{7} e^{- 7 x} cos (7 x) - \int e^{- 7 x} cos (7 x) d x)

Apply Integration By Parts

: \frac{1}{7} e^{- 7 x} sin (7 x) - \int - e^{- 7 x} sin (7 x) d x

= 49 (- \frac{1}{7} e^{- 7 x} cos (7 x) - (\frac{1}{7} e^{- 7 x} sin (7 x) - \int - e^{- 7 x} sin (7 x) d x))

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 49 (- \frac{1}{7} e^{- 7 x} cos (7 x) - (\frac{1}{7} e^{- 7 x} sin (7 x) - (- \int e^{- 7 x} sin (7 x) d x)))

Therefore

49 \cdot \int e^{- 7 x} sin (7 x) d x = 49 (- \frac{1}{7} e^{- 7 x} cos (7 x) - (\frac{1}{7} e^{- 7 x} sin (7 x) - (- \int e^{- 7 x} sin (7 x) d x)))

Isolate

\int e^{- 7 x} sin (7 x) d x

= 49 (- \frac{e ^{- 7 x} cos ( 7 x )}{14} - \frac{e ^{- 7 x} sin ( 7 x )}{14})

Add a constant to the solution

= 49 (- \frac{e ^{- 7 x} cos ( 7 x )}{14} - \frac{e ^{- 7 x} sin ( 7 x )}{14}) + C

\frac{\partial}{\partial x} (cos (6 y - 2 x))

\frac{\partial}{\partial x} (y^{6} cos (6 x) \cdot 6)

y = \frac{1}{( 7 x + 16 ) ^{4}}

7 sec (x)

\frac{\partial}{\partial x} (\frac{y}{y - 4 x})

What is the integral of 49e^{-7x}sin(7x) ?
The integral of 49e^{-7x}sin(7x) is 49(-(e^{-7x}cos(7x))/(14)-(e^{-7x}sin(7x))/(14))+C