en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1+t)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

= \int 1 + 2 t + t^{2} 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 1 d t + \int 2 t d t + \int t^{2} d t

\int 1 d t = t

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

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

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

Add a constant to the solution

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

Popular Examples

tangent of 2/(sqrt(x+5)),\at x=4 tangent of

\frac{2}{x + 5}, at x = 4

tangent of f(x)=2x^2-x-3,\at x=1 tangent of

f (x) = 2 x^{2} - x - 3, at x = 1

derivative of y=sqrt(2-6x)derivative of

y = 2 - 6 x

derivative of y=(2x+4)/(1-x)derivative of

y = \frac{2 x + 4}{1 - x}

3 y^{^{''}} + 2 y^{^{'}} = 0

Frequently Asked Questions (FAQ)

What is the integral of (1+t)^2 ?
The integral of (1+t)^2 is t+t^2+(t^3)/3+C