What is the integral of y=x^3(e^3)^4 ?

The integral of y=x^3(e^3)^4 is (e^{12}x^4)/4+C

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integral of y=x^3(e^3)^4

integral

y = x^{3} (e^{3})^{4}

\frac{e ^{12} x ^{4}}{4} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (e^{3})^{4} \cdot \int x^{3} d x

(e^{3})^{4} = e^{12}

= e^{12} \cdot \int x^{3} d x

Apply the Power Rule

= e^{12} \frac{x ^{4}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{12} x ^{4}}{4}

Add a constant to the solution

= \frac{e ^{12} x ^{4}}{4} + C

What is the integral of y=x^3(e^3)^4 ?
The integral of y=x^3(e^3)^4 is (e^{12}x^4)/4+C