What is the integral of (x^6+e^{3x}) ?

The integral of (x^6+e^{3x}) is (x^7)/7+1/3 e^{3x}+C

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integral of (x^6+e^{3x})

\int (x^{6} + e^{3 x}) d x

\frac{x ^{7}}{7} + \frac{1}{3} e^{3 x} + C

Solution steps

\int x^{6} + e^{3 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 x^{6} d x + \int e^{3 x} d x

\int x^{6} d x = \frac{x ^{7}}{7}

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

= \frac{x ^{7}}{7} + \frac{1}{3} e^{3 x}

Add a constant to the solution

= \frac{x ^{7}}{7} + \frac{1}{3} e^{3 x} + C

\frac{d}{d x} (\frac{x ^{3}}{3} + 7 x^{2} + 49 x)

x \to m lim (x - [x])

\int 5 r e^{\frac{r}{2}} d r

f (x) = x^{2} ln (8 - 5 x^{2})

y = x^{3} - 10 x, y = 6 x

What is the integral of (x^6+e^{3x}) ?
The integral of (x^6+e^{3x}) is (x^7)/7+1/3 e^{3x}+C