What is the integral of ((4+x)/2)^3 ?

The integral of ((4+x)/2)^3 is 1/32 (4+x)^4+C

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integral of ((4+x)/2)^3

integral

(\frac{4 + x}{2})^{3}

\frac{1}{32} (4 + x)^{4} + C

Solution steps

\int (\frac{4 + x}{2})^{3} d x

Simplify

(\frac{4 + x}{2})^{3} : \frac{1}{8} (4 + x)^{3}

= \int \frac{1}{8} (4 + x)^{3} d x

Take the constant out:

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

= \frac{1}{8} \cdot \int (4 + x)^{3} d x

Apply u-substitution

: \int u^{3} d u

= \frac{1}{8} \cdot \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{1}{8} \cdot \frac{u ^{4}}{4}

Substitute back

u = 4 + x

= \frac{1}{8} \cdot \frac{( 4 + x ) ^{4}}{4}

Simplify

\frac{1}{8} \cdot \frac{( 4 + x ) ^{4}}{4} : \frac{1}{32} (4 + x)^{4}

= \frac{1}{32} (4 + x)^{4}

Add a constant to the solution

= \frac{1}{32} (4 + x)^{4} + C

\frac{u}{( 1 + u ^{2} )}

\frac{2 tan ( x )}{( 1 + 2 tan ^{2} ( x ) )}

\frac{( x + 1 ) ^{2}}{( x - 1 ) ^{2}}

tan (2 - 3 x)

e^{x^{2}} x^{2}

What is the integral of ((4+x)/2)^3 ?
The integral of ((4+x)/2)^3 is 1/32 (4+x)^4+C