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}

Add a constant to the solution

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

\int \frac{6 x}{3 x ^{2} + 1} d x

\int \frac{5 x + 1}{4 x ^{2} + 4 x + 2} d x

\int (2 x^{5} - 7 x^{3} + 6) d x

\int (\frac{1}{2 x - 1}) d x

\int e^{- 3 t} cos (t) d t

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