What is the integral of 5x^3+3x+7 ?

The integral of 5x^3+3x+7 is (5x^4)/4+(3x^2)/2+7x+C

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integral of 5x^3+3x+7

\int 5 x^{3} + 3 x + 7 d x

\frac{5 x ^{4}}{4} + \frac{3 x ^{2}}{2} + 7 x + C

Solution steps

\int 5 x^{3} + 3 x + 7 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 5 x^{3} d x + \int 3 x d x + \int 7 d x

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

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

\int 7 d x = 7 x

= \frac{5 x ^{4}}{4} + \frac{3 x ^{2}}{2} + 7 x

Add a constant to the solution

= \frac{5 x ^{4}}{4} + \frac{3 x ^{2}}{2} + 7 x + C

\frac{d}{d t} (a cos (t))

x \to 0 lim (- \frac{ln ( 1 + 6 x )}{x})

\int (4 x^{6} - 2 x^{3} + 7 x - 4) d x

\frac{\partial}{\partial x} (\frac{x}{r})

f (t) = \frac{t sin ( t )}{1 + t}

What is the integral of 5x^3+3x+7 ?
The integral of 5x^3+3x+7 is (5x^4)/4+(3x^2)/2+7x+C