What is the integral of (6x^5+7x) ?

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

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integral of (6x^5+7x)

\int (6 x^{5} + 7 x) d x

x^{6} + \frac{7 x ^{2}}{2} + C

Solution steps

\int 6 x^{5} + 7 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

= \int 6 x^{5} d x + \int 7 x d x

\int 6 x^{5} d x = x^{6}

\int 7 x d x = \frac{7 x ^{2}}{2}

= x^{6} + \frac{7 x ^{2}}{2}

Add a constant to the solution

= x^{6} + \frac{7 x ^{2}}{2} + C

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

\frac{d y}{d x} = \frac{y ^{2}}{e ^{x}}, y (0) = - 2

y = x^{2}, (0, - 4)

x \to \infty lim (\frac{x}{ln ( x )})

\frac{d}{d x} (\frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}})