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

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