What is the integral of 30(x+9)(x+9)^4 ?

The integral of 30(x+9)(x+9)^4 is 5(x+9)^6+C

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integral of 30(x+9)(x+9)^4

\int 30 (x + 9) (x + 9)^{4} d x

5 (x + 9)^{6} + C

Solution steps

\int 30 (x + 9) (x + 9)^{4} d x

Take the constant out:

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

= 30 \cdot \int (x + 9) (x + 9)^{4} d x

Simplify

(x + 9) (x + 9)^{4} : (x + 9)^{5}

= 30 \cdot \int (x + 9)^{5} d x

Apply u-substitution

: \int u^{5} d u

= 30 \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= 30 \cdot \frac{u ^{6}}{6}

Substitute back

u = x + 9

= 30 \cdot \frac{( x + 9 ) ^{6}}{6}

Simplify

30 \cdot \frac{( x + 9 ) ^{6}}{6} : 5 (x + 9)^{6}

= 5 (x + 9)^{6}

Add a constant to the solution

= 5 (x + 9)^{6} + C

\frac{d}{d x} (\frac{x ^{3}}{2} - \frac{3}{x ^{2}})

y^{^{''}} - 7 y^{^{'}} + 10 y = - 2 cos (2 t)

f (x) = 4 x - 1

\frac{d y}{d x} = 8 e^{x - y}

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

What is the integral of 30(x+9)(x+9)^4 ?
The integral of 30(x+9)(x+9)^4 is 5(x+9)^6+C