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

The integral of ((1+sqrt(x))^4)/(sqrt(x)) is 2/5 (1+sqrt(x))^5+C

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

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

\frac{2}{5} (1 + x)^{5} + C

Solution steps

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

Apply u-substitution

: \int 2 u^{4} d u

= \int 2 u^{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 2 \cdot \frac{u ^{5}}{5}

Substitute back

u = 1 + x

= 2 \cdot \frac{( 1 + x ) ^{5}}{5}

Simplify

2 \cdot \frac{( 1 + x ) ^{5}}{5} : \frac{2}{5} (1 + x)^{5}

= \frac{2}{5} (1 + x)^{5}

Add a constant to the solution

= \frac{2}{5} (1 + x)^{5} + C

\frac{d}{d x} (\frac{2}{1 + e ^{x}})

n = 0 \sum \infty \frac{n + 1}{n}

\int sec^{4} (\frac{t}{2}) d t

\int x^{2} (x - 1)^{2} d x

\frac{2}{( 3 x + 1 )}, x = 2

What is the integral of ((1+sqrt(x))^4)/(sqrt(x)) ?
The integral of ((1+sqrt(x))^4)/(sqrt(x)) is 2/5 (1+sqrt(x))^5+C