What is the integral of 2(x^2+2x)^{16}(2x+2) ?

The integral of 2(x^2+2x)^{16}(2x+2) is 2/17 (x^2+2x)^{17}+C

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integral of 2(x^2+2x)^{16}(2x+2)

\int 2 (x^{2} + 2 x)^{16} (2 x + 2) d x

\frac{2}{17} (x^{2} + 2 x)^{17} + C

Solution steps

\int 2 (x^{2} + 2 x)^{16} (2 x + 2) d x

Take the constant out:

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

= 2 \cdot \int (x^{2} + 2 x)^{16} (2 x + 2) d x

Apply u-substitution

: \int u^{16} d u

= 2 \cdot \int u^{16} d u

Apply the Power Rule

: \frac{u ^{17}}{17}

= 2 \cdot \frac{u ^{17}}{17}

Substitute back

u = x^{2} + 2 x

= 2 \cdot \frac{( x ^{2} + 2 x ) ^{17}}{17}

Simplify

2 \cdot \frac{( x ^{2} + 2 x ) ^{17}}{17} : \frac{2}{17} (x^{2} + 2 x)^{17}

= \frac{2}{17} (x^{2} + 2 x)^{17}

Add a constant to the solution

= \frac{2}{17} (x^{2} + 2 x)^{17} + C

\frac{2 s}{( s ^{2} + 2 s + 6 )}

f (x) = 3^{x^{2} - 1}, at x = 2

y^{^{''}} - y = 4 sin (3 t)

\int - 2 x^{4} - 4 x^{2} - 5 d x

\frac{d}{d x} (cot (\frac{π}{2}))

What is the integral of 2(x^2+2x)^{16}(2x+2) ?
The integral of 2(x^2+2x)^{16}(2x+2) is 2/17 (x^2+2x)^{17}+C