What is the integral of 2x^2cos(2pi)x^3 ?

The integral of 2x^2cos(2pi)x^3 is (x^6)/3+C

integral of 2x^2cos(2pi)x^3

\int 2 x^{2} cos (2 π) x^{3} d x

\frac{x ^{6}}{3} + C

Solution steps

\int 2 x^{2} cos (2 π) x^{3} d x

Take the constant out:

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

= 2 cos (2 π) \cdot \int x^{2} x^{3} d x

2 cos (2 π) = 2

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

Simplify

x^{2} x^{3} : x^{5}

= 2 \cdot \int x^{5} d x

Apply the Power Rule

= 2 \cdot \frac{x ^{6}}{6}

Simplify

2 \cdot \frac{x ^{6}}{6} : \frac{x ^{6}}{3}

= \frac{x ^{6}}{3}

Add a constant to the solution

= \frac{x ^{6}}{3} + C

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What is the integral of 2x^2cos(2pi)x^3 ?
The integral of 2x^2cos(2pi)x^3 is (x^6)/3+C