What is the integral of x^5ex^6+1 ?

The integral of x^5ex^6+1 is (ex^{12})/(12)+x+C

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integral of x^5ex^6+1

\int x^{5} e x^{6} + 1 d x

\frac{e x ^{12}}{12} + x + C

Solution steps

\int x^{5} e x^{6} + 1 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^{5} e x^{6} d x + \int 1 d x

\int x^{5} e x^{6} d x = \frac{e x ^{12}}{12}

\int 1 d x = x

= \frac{e x ^{12}}{12} + x

Add a constant to the solution

= \frac{e x ^{12}}{12} + x + C

f (x) = - 5 x^{4}

\int (cos (2 x) e^{2 x}) d x

\int \frac{x + 2}{( x ^{2} + 2 x + 10 ) ^{\frac{5}{2}}} d x

f (x) = 5 x^{4}

\frac{e ^{x}}{x cos ( x )}

What is the integral of x^5ex^6+1 ?
The integral of x^5ex^6+1 is (ex^{12})/(12)+x+C