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Popular >

integral from 0 to 1 of x(x^2+1)

Solution

\int_{0}^{1} x (x^{2} + 1) d x

Solution

\frac{3}{4}

+1

Decimal Notation

0.75

Solution steps

\int_{0}^{1} x (x^{2} + 1) d x

Expand

x (x^{2} + 1) : x^{3} + x

= \int_{0}^{1} 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_{0}^{1} x^{3} d x + \int_{0}^{1} x d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} x d x = \frac{1}{2}

= \frac{1}{4} + \frac{1}{2}

Simplify

\frac{1}{4} + \frac{1}{2} : \frac{3}{4}

= \frac{3}{4}

Popular Examples

integral of-tsqrt(t-1)

\int - t t - 1 d t

integral of (6e^u-u^3(sqrt(u)+1))

\int (6 e^{u} - u^{3} (u + 1)) d u

(\partial)/(\partial x)(x/(x^2+1))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 1})

derivative of (3x+2/(x-3))

\frac{d}{d x} (\frac{3 x + 2}{x - 3})

integral of 1/(2x^2-16)

\int \frac{1}{2 x ^{2} - 16} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(x^2+1) ?
The integral from 0 to 1 of x(x^2+1) is 3/4