What is the integral of 7x^6+6x^2+2sqrt(x) ?

The integral of 7x^6+6x^2+2sqrt(x) is x^7+2x^3+4/3 x^{3/2}+C

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integral of 7x^6+6x^2+2sqrt(x)

\int 7 x^{6} + 6 x^{2} + 2 x d x

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

Solution steps

\int 7 x^{6} + 6 x^{2} + 2 x 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 7 x^{6} d x + \int 6 x^{2} d x + \int 2 x d x

\int 7 x^{6} d x = x^{7}

\int 6 x^{2} d x = 2 x^{3}

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

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

Add a constant to the solution

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

What is the integral of 7x^6+6x^2+2sqrt(x) ?
The integral of 7x^6+6x^2+2sqrt(x) is x^7+2x^3+4/3 x^{3/2}+C