What is the integral of 5+(3x^2)/(sqrt(2x^3+7)) ?

The integral of 5+(3x^2)/(sqrt(2x^3+7)) is 5x+sqrt(2x^3+7)+C

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integral of 5+(3x^2)/(sqrt(2x^3+7))

\int 5 + \frac{3 x ^{2}}{2 x ^{3} + 7} d x

5 x + 2 x^{3} + 7 + C

Solution steps

\int 5 + \frac{3 x ^{2}}{2 x ^{3} + 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 5 d x + \int \frac{3 x ^{2}}{2 x ^{3} + 7} d x

\int 5 d x = 5 x

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

= 5 x + 2 x^{3} + 7

Add a constant to the solution

= 5 x + 2 x^{3} + 7 + C

\int 300 t e^{\frac{- t ^{2}}{7}} d t

x \to 0 lim (\frac{cos ( 5 x )}{x})

\frac{\partial}{\partial x} (6 x^{2} + y^{2} - 7 y)

e^{- 6 s}

\frac{\partial}{\partial x} (56 y e^{8 x})

What is the integral of 5+(3x^2)/(sqrt(2x^3+7)) ?
The integral of 5+(3x^2)/(sqrt(2x^3+7)) is 5x+sqrt(2x^3+7)+C