What is the integral of 2x(x^2+14)^9 ?

The integral of 2x(x^2+14)^9 is 1/10 (x^2+14)^{10}+C

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integral of 2x(x^2+14)^9

\int 2 x (x^{2} + 14)^{9} d x

\frac{1}{10} (x^{2} + 14)^{10} + C

Solution steps

\int 2 x (x^{2} + 14)^{9} d x

Take the constant out:

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

= 2 \cdot \int x (x^{2} + 14)^{9} d x

Apply u-substitution

: \int \frac{u ^{9}}{2} d u

= 2 \cdot \int \frac{u ^{9}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{10}}{10}

Substitute back

u = x^{2} + 14

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 14 ) ^{10}}{10}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 14 ) ^{10}}{10} : \frac{1}{10} (x^{2} + 14)^{10}

= \frac{1}{10} (x^{2} + 14)^{10}

Add a constant to the solution

= \frac{1}{10} (x^{2} + 14)^{10} + C

\frac{( d y )}{( d x )} = \frac{x}{y}

\int_{1}^{2} (ln (x))^{2} d x

y = - x, x = - 1, x = 2, y = 0

y^{^{''}} + 8 y^{^{'}} + 65 y = 455, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{1}{x ^{2} + 6 x + 18} d x

What is the integral of 2x(x^2+14)^9 ?
The integral of 2x(x^2+14)^9 is 1/10 (x^2+14)^{10}+C