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

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

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integral of (3x^4-5x)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (6 x + 29 cos (\frac{3 x}{4}) + 5 x^{2} + 3)

\int (2 x - 3)^{5} d x

y \to x lim (\frac{y ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{y - x})

f (x) = x^{2}, at x = 5

\int 1 - cos (4 x) d x

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