What is the integral of 4x^2+3x+2*2(x+1) ?

The integral of 4x^2+3x+2*2(x+1) is (4x^3)/3+(7x^2)/2+4x+C

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integral of 4x^2+3x+2*2(x+1)

integral

4 x^{2} + 3 x + 2 \cdot 2 (x + 1)

\frac{4 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 4 x + C

Solution steps

\int 4 x^{2} + 3 x + 2 \cdot 2 (x + 1) d x

Simplify

4 x^{2} + 3 x + 2 \cdot 2 (x + 1) : 4 x^{2} + 7 x + 4

= \int 4 x^{2} + 7 x + 4 d x

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 x^{2} d x + \int 7 x d x + \int 4 d x

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 4 d x = 4 x

= \frac{4 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 4 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 4 x + C

(8 x - x^{4})^{3} (8 x^{3} - 16)

cos^{2} (\frac{x}{4})

(\frac{1}{x ^{4}}) sin (x)

cos ((\frac{1}{4}) x)

(t^{2} - 6 t + 13)^{- 1}

What is the integral of 4x^2+3x+2*2(x+1) ?
The integral of 4x^2+3x+2*2(x+1) is (4x^3)/3+(7x^2)/2+4x+C