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Popular >

integral of (2u+1)^2

Solution

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

Solution

\frac{4 u ^{3}}{3} + 2 u^{2} + u + C

Solution steps

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

Expand

(2 u + 1)^{2} : 4 u^{2} + 4 u + 1

= \int 4 u^{2} + 4 u + 1 d u

Apply the Sum Rule:

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

= \int 4 u^{2} d u + \int 4 u d u + \int 1 d u

\int 4 u^{2} d u = \frac{4 u ^{3}}{3}

\int 4 u d u = 2 u^{2}

\int 1 d u = u

= \frac{4 u ^{3}}{3} + 2 u^{2} + u

Add a constant to the solution

= \frac{4 u ^{3}}{3} + 2 u^{2} + u + C

Popular Examples

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

f (x) = \frac{x}{1 + x ^{2}}, at x = 3

taylor 5x^2+3x^4 taylor

5 x^{2} + 3 x^{4}

inverse oflaplace ((2))/((s-1)^2)inverse laplace

\frac{( 2 )}{( s - 1 ) ^{2}}

inverse oflaplace 2cos(5t)inverse laplace

2 cos (5 t)

inverse oflaplace (s+2)^2 inverse laplace

(s + 2)^{2}

Frequently Asked Questions (FAQ)

What is the integral of (2u+1)^2 ?
The integral of (2u+1)^2 is (4u^3)/3+2u^2+u+C