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Popular >

integral of (y+1)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

Apply the Sum Rule:

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

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

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

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

\int 1 d y = y

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 0 of (e^{8x}-1)/x

x \to 0 lim (\frac{e ^{8 x} - 1}{x})

slope ofintercept (2,1),(-4,-2)slope intercept

(2, 1), (- 4, - 2)

integral of 4x^2cos(x/5)

\int 4 x^{2} cos (\frac{x}{5}) d x

limit as x approaches 3-of 2/((x-3)^3)

x \to 3 - lim (\frac{2}{( x - 3 ) ^{3}})

integral of (sqrt(x)-5)/(sqrt(x)+3)

\int \frac{x - 5}{x + 3} d x

Frequently Asked Questions (FAQ)

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