What is the integral of 7x(x^3+6) ?

The integral of 7x(x^3+6) is 7((x^5)/5+3x^2)+C

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integral of 7x(x^3+6)

\int 7 x (x^{3} + 6) d x

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

Solution steps

\int 7 x (x^{3} + 6) d x

Take the constant out:

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

= 7 \cdot \int x (x^{3} + 6) d x

Expand

x (x^{3} + 6) : x^{4} + 6 x

= 7 \cdot \int x^{4} + 6 x d x

Apply the Sum Rule:

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

= 7 (\int x^{4} d x + \int 6 x d x)

\int x^{4} d x = \frac{x ^{5}}{5}

\int 6 x d x = 3 x^{2}

= 7 (\frac{x ^{5}}{5} + 3 x^{2})

Add a constant to the solution

= 7 (\frac{x ^{5}}{5} + 3 x^{2}) + C

\frac{d}{d t} (1 - e^{- t})

\frac{\partial}{\partial x} (in x y)

y^{^{'}} (t) = (y - 1) (y + 1), y (0) = 3

x \to 14 lim (7 - tan (7))

\int sin (1 - 3 x) d x

What is the integral of 7x(x^3+6) ?
The integral of 7x(x^3+6) is 7((x^5)/5+3x^2)+C