What is the integral of 3x^2+5sin(x)-3e^x ?

The integral of 3x^2+5sin(x)-3e^x is x^3-5cos(x)-3e^x+C

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integral of 3x^2+5sin(x)-3e^x

\int 3 x^{2} + 5 sin (x) - 3 e^{x} d x

x^{3} - 5 cos (x) - 3 e^{x} + C

Solution steps

\int 3 x^{2} + 5 sin (x) - 3 e^{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 x^{2} d x + \int 5 sin (x) d x - \int 3 e^{x} d x

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

\int 5 sin (x) d x = - 5 cos (x)

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

= x^{3} - 5 cos (x) - 3 e^{x}

Add a constant to the solution

= x^{3} - 5 cos (x) - 3 e^{x} + C

What is the integral of 3x^2+5sin(x)-3e^x ?
The integral of 3x^2+5sin(x)-3e^x is x^3-5cos(x)-3e^x+C