en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of t^2+t

Solution

\int t^{2} + t d t

Solution

\frac{t ^{3}}{3} + \frac{t ^{2}}{2} + C

Solution steps

\int t^{2} + 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^{2} d t + \int t d t

\int t^{2} d t = \frac{t ^{3}}{3}

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

= \frac{t ^{3}}{3} + \frac{t ^{2}}{2}

Add a constant to the solution

= \frac{t ^{3}}{3} + \frac{t ^{2}}{2} + C

Graph

Popular Examples

\int 50 d x

integral of |t-1|

\int ∣ t - 1 ∣ d t

integral of 20cos(w)e^{-2w}

\int 20 cos (w) e^{- 2 w} d w

integral of (x+3)ln(2x)

\int (x + 3) ln (2 x) d x

integral of (arctan(x/2))/(x^2+4)

\int \frac{arctan ( \frac{x}{2} )}{x ^{2} + 4} d x

Frequently Asked Questions (FAQ)

What is the integral of t^2+t ?
The integral of t^2+t is (t^3)/3+(t^2)/2+C