What is the integral of 4x^3-9+2sin(x)+7e^x ?

The integral of 4x^3-9+2sin(x)+7e^x is x^4-9x-2cos(x)+7e^x+C

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integral of 4x^3-9+2sin(x)+7e^x

\int 4 x^{3} - 9 + 2 sin (x) + 7 e^{x} d x

x^{4} - 9 x - 2 cos (x) + 7 e^{x} + C

Solution steps

\int 4 x^{3} - 9 + 2 sin (x) + 7 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 4 x^{3} d x - \int 9 d x + \int 2 sin (x) d x + \int 7 e^{x} d x

\int 4 x^{3} d x = x^{4}

\int 9 d x = 9 x

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

\int 7 e^{x} d x = 7 e^{x}

= x^{4} - 9 x - 2 cos (x) + 7 e^{x}

Add a constant to the solution

= x^{4} - 9 x - 2 cos (x) + 7 e^{x} + C

What is the integral of 4x^3-9+2sin(x)+7e^x ?
The integral of 4x^3-9+2sin(x)+7e^x is x^4-9x-2cos(x)+7e^x+C