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Popular >

integral of x^4-4x^2

Solution

\int x^{4} - 4 x^{2} d x

Solution

\frac{x ^{5}}{5} - \frac{4 x ^{3}}{3} + C

Solution steps

\int x^{4} - 4 x^{2} 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 x^{4} d x - \int 4 x^{2} d x

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

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

= \frac{x ^{5}}{5} - \frac{4 x ^{3}}{3}

Add a constant to the solution

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

Popular Examples

integral of (1-y^2)/2

\int \frac{1 - y ^{2}}{2} d y

integral of (2ysin(z))

\int (2 y sin (z)) d y

integral of (-3)/(1-3x)

\int \frac{- 3}{1 - 3 x} d x

integral of 1/(u(ln(u)-1))

\int \frac{1}{u ( ln ( u ) - 1 )} d u

integral of (1+x)/(5-4x^2)

\int \frac{1 + x}{5 - 4 x ^{2}} d x

Frequently Asked Questions (FAQ)

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