What is the integral of (3x^4+5x-6) ?

The integral of (3x^4+5x-6) is (3x^5)/5+(5x^2)/2-6x+C

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integral of (3x^4+5x-6)

\int (3 x^{4} + 5 x - 6) d x

\frac{3 x ^{5}}{5} + \frac{5 x ^{2}}{2} - 6 x + C

Solution steps

\int 3 x^{4} + 5 x - 6 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 3 x^{4} d x + \int 5 x d x - \int 6 d x

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= \frac{3 x ^{5}}{5} + \frac{5 x ^{2}}{2} - 6 x

Add a constant to the solution

= \frac{3 x ^{5}}{5} + \frac{5 x ^{2}}{2} - 6 x + C

x \to 0 lim (\frac{2 sin ( 2 x )}{x})

\frac{d}{d x} (x^{9} ln (5 x))

y y^{^{'}} + 3 y = x^{2} y

(\frac{20}{10 s + 1}) \cdot \frac{1}{s}

f (x) = ln (e^{x^{2}}), at x = 1

What is the integral of (3x^4+5x-6) ?
The integral of (3x^4+5x-6) is (3x^5)/5+(5x^2)/2-6x+C