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

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

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

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

cos (x) + e^{- x} + x^{3} + C

Solution steps

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

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

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

\int 3 x^{2} d x = x^{3}

= - (- cos (x)) - (- e^{- x}) + x^{3}

Simplify

= cos (x) + e^{- x} + x^{3}

Add a constant to the solution

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2} + e^{- x}

\frac{d y}{d x} = 2 x (y - 1)

\int \frac{7 - x ^{4}}{5 x} d x

7 x - 2 y

\frac{d y}{d x} = x y^{\frac{1}{2}}

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