en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of t(t^2+1)

Solution

\int t (t^{2} + 1) d t

Solution

\frac{t ^{4}}{4} + \frac{t ^{2}}{2} + C

Solution steps

\int t (t^{2} + 1) d t

Expand

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

= \int t^{3} + t d t

Apply the Sum Rule:

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

= \int t^{3} d t + \int t d t

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

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

= \frac{t ^{4}}{4} + \frac{t ^{2}}{2}

Add a constant to the solution

= \frac{t ^{4}}{4} + \frac{t ^{2}}{2} + C

Graph

Popular Examples

(3xy+y^2)dx+(x^2+xy)dy=0

(3 x y + y^{2}) d x + (x^{2} + x y) d y = 0

integral from 3 to 5 of 1/(sqrt(5-x))

\int_{3}^{5} \frac{1}{5 - x} d x

taylor (3.49)/(x^{0.432)}taylor

\frac{3.49}{x ^{0.432}}

derivative of 1/(3(1+x^{2/3)})

\frac{d}{d x} (\frac{1}{3 ( 1 + x ) ^{\frac{2}{3}}})

derivative of f(x)=(e^{3x}-1)^5 derivative of

f (x) = (e^{3 x} - 1)^{5}

Frequently Asked Questions (FAQ)

What is the integral of t(t^2+1) ?
The integral of t(t^2+1) is (t^4)/4+(t^2)/2+C