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Popular Calculus >

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

Graph

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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