What is the integral of ((x+5)^3)/2 ?

The integral of ((x+5)^3)/2 is 1/8 (x+5)^4+C

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integral of ((x+5)^3)/2

integral

\frac{( x + 5 ) ^{3}}{2}

\frac{1}{8} (x + 5)^{4} + C

Solution steps

\int \frac{( x + 5 ) ^{3}}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int (x + 5)^{3} d x

Apply u-substitution

: \int u^{3} d u

= \frac{1}{2} \cdot \int u^{3} d u

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{u ^{4}}{4}

Substitute back

u = x + 5

= \frac{1}{2} \cdot \frac{( x + 5 ) ^{4}}{4}

Simplify

\frac{1}{2} \cdot \frac{( x + 5 ) ^{4}}{4} : \frac{1}{8} (x + 5)^{4}

= \frac{1}{8} (x + 5)^{4}

Add a constant to the solution

= \frac{1}{8} (x + 5)^{4} + C

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

\frac{10 t}{( t + 1 ) ^{2}}

8 + x

\frac{( a ^{x} )}{( a ^{x} - 1 )}

sec^{4} (x) tan^{2} (x)

What is the integral of ((x+5)^3)/2 ?
The integral of ((x+5)^3)/2 is 1/8 (x+5)^4+C