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Popular >

integral of (t+1)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

\int 1 d t = t

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

Add a constant to the solution

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

Popular Examples

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\int_{1}^{4} (5 x + x) d x

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\int cos (1 + 5 t) d t

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\int x (arctan (x))^{2} d x

integral of (tan(x))/(cos^3(x))

\int \frac{tan ( x )}{cos ^{3} ( x )} d x

(dy)/(y^2-4)=dx

\frac{d y}{y ^{2} - 4} = d x

Frequently Asked Questions (FAQ)

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