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

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

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

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

\frac{2 x ^{5}}{5} + 2 x + C

Solution steps

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

Expand

\frac{2 x ^{5} + x}{x} : 2 x^{4} + \frac{1}{x}

= \int 2 x^{4} + \frac{1}{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 2 x^{4} d x + \int \frac{1}{x} d x

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

\int \frac{1}{x} d x = 2 x

= \frac{2 x ^{5}}{5} + 2 x

Add a constant to the solution

= \frac{2 x ^{5}}{5} + 2 x + C

\int_{- 1}^{0} x d x

\frac{d y}{d x} = 7 y e^{x + 8}

\int_{4}^{\infty} e^{- 5 x} d x

\frac{d y}{d x} = \frac{e ^{x}}{1 + e ^{x}}

y^{^{''}} + 8 y^{^{'}} + 17 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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