What is the integral of 3e^{-x}-2sin(pi/2-x) ?

The integral of 3e^{-x}-2sin(pi/2-x) is -3e^{-x}-2sin(x)+C

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integral of 3e^{-x}-2sin(pi/2-x)

\int 3 e^{- x} - 2 sin (\frac{π}{2} - x) d x

- 3 e^{- x} - 2 sin (x) + C

Solution steps

\int 3 e^{- x} - 2 sin (\frac{π}{2} - x) d x

Rewrite using trig identities

= \int 3 e^{- x} - 2 cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 e^{- x} d x - \int 2 cos (x) d x

\int 3 e^{- x} d x = - 3 e^{- x}

\int 2 cos (x) d x = 2 sin (x)

= - 3 e^{- x} - 2 sin (x)

Add a constant to the solution

= - 3 e^{- x} - 2 sin (x) + C

\frac{d}{d x} (3 x^{2} - 6 x - 9)

y = 2 sec (x) - 4 cos (x)

t \to 0 lim (\frac{e ^{4 t} - 1}{t})

5 x^{9} - 2 x^{6}

\frac{6}{s ^{5}}

What is the integral of 3e^{-x}-2sin(pi/2-x) ?
The integral of 3e^{-x}-2sin(pi/2-x) is -3e^{-x}-2sin(x)+C