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

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

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

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

3 x^{3} + 2 x + C

Solution steps

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

Simplify

(3 x)^{2} + 2 : 9 x^{2} + 2

= \int 9 x^{2} + 2 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 9 x^{2} d x + \int 2 d x

\int 9 x^{2} d x = 3 x^{3}

\int 2 d x = 2 x

= 3 x^{3} + 2 x

Add a constant to the solution

= 3 x^{3} + 2 x + C

x \to 1 lim (1 - 2 - x)

\frac{d}{d x} (arccos (x^{3}))

\frac{d}{d x} (2 \cdot x^{2})

\frac{( s - 2 )}{( s - 3 ) ( s + 1 )}

\int \frac{sin ^{7} ( 4 x )}{cos ^{4} ( 4 x )} d x

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