What is the integral of 3(x+10)^3 ?

The integral of 3(x+10)^3 is 3/4 (x+10)^4+C

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integral of 3(x+10)^3

\int 3 (x + 10)^{3} d x

\frac{3}{4} (x + 10)^{4} + C

Solution steps

\int 3 (x + 10)^{3} d x

Take the constant out:

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

= 3 \cdot \int (x + 10)^{3} d x

Apply u-substitution

= 3 \cdot \int u^{3} d u

Apply the Power Rule

= 3 \cdot \frac{u ^{4}}{4}

Substitute back

u = x + 10

= 3 \cdot \frac{( x + 10 ) ^{4}}{4}

Simplify

3 \cdot \frac{( x + 10 ) ^{4}}{4} : \frac{3}{4} (x + 10)^{4}

= \frac{3}{4} (x + 10)^{4}

Add a constant to the solution

= \frac{3}{4} (x + 10)^{4} + C