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Popular >

integral of (u+u^4)

Solution

\int (u + u^{4}) d u

Solution

\frac{u ^{2}}{2} + \frac{u ^{5}}{5} + C

Solution steps

\int u + u^{4} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u + \int u^{4} d u

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

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

= \frac{u ^{2}}{2} + \frac{u ^{5}}{5}

Add a constant to the solution

= \frac{u ^{2}}{2} + \frac{u ^{5}}{5} + C

Popular Examples

integral from 1 to 1000 of (33)/(x^3)

\int_{1}^{1000} \frac{33}{x ^{3}} d x

integral from-5 to 5 of (25-x^2)

\int_{- 5}^{5} (25 - x^{2}) d x

integral of x/(16)

\int \frac{x}{16} d x

(\partial)/(\partial x)((2x+y)/(y-x))

\frac{\partial}{\partial x} (\frac{2 x + y}{y - x})

integral of (64x^2)/(x^4-40x^2+144)

\int \frac{64 x ^{2}}{x ^{4} - 40 x ^{2} + 144} d x

Frequently Asked Questions (FAQ)

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