What is the integral of 3x^4-5sqrt(x)+1 ?

The integral of 3x^4-5sqrt(x)+1 is (3x^5)/5-10/3 x^{3/2}+x+C

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integral of 3x^4-5sqrt(x)+1

\int 3 x^{4} - 5 x + 1 d x

\frac{3 x ^{5}}{5} - \frac{10}{3} x^{\frac{3}{2}} + x + C

Solution steps

\int 3 x^{4} - 5 x + 1 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 3 x^{4} d x - \int 5 x d x + \int 1 d x

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

\int 1 d x = x

= \frac{3 x ^{5}}{5} - \frac{10}{3} x^{\frac{3}{2}} + x

Add a constant to the solution

= \frac{3 x ^{5}}{5} - \frac{10}{3} x^{\frac{3}{2}} + x + C

What is the integral of 3x^4-5sqrt(x)+1 ?
The integral of 3x^4-5sqrt(x)+1 is (3x^5)/5-10/3 x^{3/2}+x+C