What is the integral of 5ab^2x^3 ?

The integral of 5ab^2x^3 is (5ab^2x^4)/4+C

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integral of 5ab^2x^3

\int 5 a b^{2} x^{3} d x

\frac{5 a b ^{2} x ^{4}}{4} + C

Solution steps

\int 5 a b^{2} x^{3} d x

Take the constant out:

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

= 5 a b^{2} \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= 5 a b^{2} \frac{x ^{4}}{4}

Multiply fractions:

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

= \frac{5 a b ^{2} x ^{4}}{4}

Add a constant to the solution

= \frac{5 a b ^{2} x ^{4}}{4} + C

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