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Popular >

integral of 3x^3-x

Solution

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

Solution

\frac{3 x ^{4}}{4} - \frac{x ^{2}}{2} + C

Solution steps

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

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

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

= \frac{3 x ^{4}}{4} - \frac{x ^{2}}{2}

Add a constant to the solution

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

Popular Examples

integral of ((sqrt(x))/3+8/(sqrt(x)))

\int (\frac{x}{3} + \frac{8}{x}) d x

integral of (5x)/(x^2-25)

\int \frac{5 x}{x ^{2} - 25} d x

integral of (sqrt(epi)cos(t)+5/(e+et^2))

\int (e π cos (t) + \frac{5}{e + e t ^{2}}) d t

integral of cos(x+4y)

\int cos (x + 4 y) d x

integral of 7-5x

\int 7 - 5 x d x

Frequently Asked Questions (FAQ)

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