What is the integral of (2x^2+3x+7) ?

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

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integral of (2x^2+3x+7)

\int (2 x^{2} + 3 x + 7) d x

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

Solution steps

\int 2 x^{2} + 3 x + 7 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 2 x^{2} d x + \int 3 x d x + \int 7 d x

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

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

\int 7 d x = 7 x

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

Add a constant to the solution

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

y = x^{2} - 3, (- 1, - 2)

f (x) = 7 x^{3} e^{- x}

\int \frac{1}{y ^{\frac{1}{2}}} d y

\int e^{2 x} sin (e^{2 x}) d x

\int 4 t^{3} + t d t

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