What is the integral of (x+1/(x^4sqrt(x))) ?

The integral of (x+1/(x^4sqrt(x))) is (x^2)/2-2/(7x^{7/2)}+C

Popular >

integral of (x+1/(x^4sqrt(x)))

\int (x + \frac{1}{x ^{4} x}) d x

\frac{x ^{2}}{2} - \frac{2}{7 x ^{\frac{7}{2}}} + C

Solution steps

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

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

\int \frac{1}{x ^{4} x} d x = - \frac{2}{7 x ^{\frac{7}{2}}}

= \frac{x ^{2}}{2} - \frac{2}{7 x ^{\frac{7}{2}}}

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{2}{7 x ^{\frac{7}{2}}} + C

\int sec^{8} (x) d x

\frac{\partial}{\partial x} (40 x y \cdot e^{5 x^{2} - 2 y})

\int \frac{1}{4} x^{3} d x

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

y^{^{'}} = \frac{1 - y ^{2}}{e ^{x}}

What is the integral of (x+1/(x^4sqrt(x))) ?
The integral of (x+1/(x^4sqrt(x))) is (x^2)/2-2/(7x^{7/2)}+C