en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of x(x^2+5)

Solution

\int_{0}^{1} x (x^{2} + 5) d x

Solution

\frac{11}{4}

+1

Decimal

2.75

Solution steps

\int_{0}^{1} x (x^{2} + 5) d x

Expand

x (x^{2} + 5) : x^{3} + 5 x

= \int_{0}^{1} x^{3} + 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_{0}^{1} x^{3} d x + \int_{0}^{1} 5 x d x

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

\int_{0}^{1} 5 x d x = \frac{5}{2}

= \frac{1}{4} + \frac{5}{2}

Simplify

\frac{1}{4} + \frac{5}{2} : \frac{11}{4}

= \frac{11}{4}

Graph

Popular Examples

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

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

integral from 0 to T of x

\int_{0}^{T} x d x

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

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

integral from 0 to 2 of (5x^3-6x-2)

\int_{0}^{2} (5 x^{3} - 6 x - 2) d x

integral from 0 to 1 of x^3(x^4-4)^6

\int_{0}^{1} x^{3} (x^{4} - 4)^{6} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(x^2+5) ?
The integral from 0 to 1 of x(x^2+5) is 11/4