What is the integral of (x-3)(x+11)^{15} ?

The integral of (x-3)(x+11)^{15} is ((x+11)^{17}}{17}-\frac{7(x+11)^{16})/8+C

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integral of (x-3)(x+11)^{15}

\int (x - 3) (x + 11)^{15} d x

\frac{( x + 11 ) ^{17}}{17} - \frac{7 ( x + 11 ) ^{16}}{8} + C

Solution steps

\int (x - 3) (x + 11)^{15} d x

Apply u-substitution

: \int u^{15} (u - 14) d u

= \int u^{15} (u - 14) d u

Expand

u^{15} (u - 14) : u^{16} - 14 u^{15}

= \int u^{16} - 14 u^{15} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{16} d u - \int 14 u^{15} d u

\int u^{16} d u = \frac{u ^{17}}{17}

\int 14 u^{15} d u = \frac{7 u ^{16}}{8}

= \frac{u ^{17}}{17} - \frac{7 u ^{16}}{8}

Substitute back

u = x + 11

= \frac{( x + 11 ) ^{17}}{17} - \frac{7 ( x + 11 ) ^{16}}{8}

Add a constant to the solution

= \frac{( x + 11 ) ^{17}}{17} - \frac{7 ( x + 11 ) ^{16}}{8} + C

y = \frac{x ^{6}}{f ( x )}

\int x^{2} x - 1 d x

f (x) = x + 2

\frac{\partial}{\partial x} (3 y^{2} + x^{2} - 3)

y^{^{'}} = cos (2 x)

What is the integral of (x-3)(x+11)^{15} ?
The integral of (x-3)(x+11)^{15} is ((x+11)^{17}}{17}-\frac{7(x+11)^{16})/8+C