What is the integral of 3x^2× 4x^4 ?

The integral of 3x^2× 4x^4 is (12x^7)/7+C

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integral of 3x^2× 4x^4

\int 3 x^{2} \cdot 4 x^{4} d x

\frac{12 x ^{7}}{7} + C

Solution steps

\int 3 x^{2} \cdot 4 x^{4} d x

Take the constant out:

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

= 3 \cdot 4 \cdot \int x^{2} x^{4} d x

Simplify

= 12 \cdot \int x^{2} x^{4} d x

Simplify

x^{2} x^{4} : x^{6}

= 12 \cdot \int x^{6} d x

Apply the Power Rule

= 12 \cdot \frac{x ^{7}}{7}

Multiply fractions:

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

= \frac{12 x ^{7}}{7}

Add a constant to the solution

= \frac{12 x ^{7}}{7} + C