What is the integral of e^{3x+9}-3x^2 ?

The integral of e^{3x+9}-3x^2 is 1/3 e^{3x+9}-x^3+C

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integral of e^{3x+9}-3x^2

\int e^{3 x + 9} - 3 x^{2} d x

\frac{1}{3} e^{3 x + 9} - x^{3} + C

Solution steps

\int e^{3 x + 9} - 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 e^{3 x + 9} d x - \int 3 x^{2} d x

\int e^{3 x + 9} d x = \frac{1}{3} e^{3 x + 9}

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

= \frac{1}{3} e^{3 x + 9} - x^{3}

Add a constant to the solution

= \frac{1}{3} e^{3 x + 9} - x^{3} + C

y^{^{''}} + 4 y = 8

\int 2 + cos (x) d x

x \to 2 lim (3 x^{2} - 7 x + 5)

\int sec^{4} (3 x) d x

\int_{- 3}^{3} \frac{1}{9 - x ^{2}} d x

What is the integral of e^{3x+9}-3x^2 ?
The integral of e^{3x+9}-3x^2 is 1/3 e^{3x+9}-x^3+C