What is the integral of ((1+sqrt(x))^9)/(sqrt(x)) ?

The integral of ((1+sqrt(x))^9)/(sqrt(x)) is 1/5 (1+sqrt(x))^{10}+C

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integral of ((1+sqrt(x))^9)/(sqrt(x))

\int \frac{( 1 + x ) ^{9}}{x} d x

\frac{1}{5} (1 + x)^{10} + C

Solution steps

\int \frac{( 1 + x ) ^{9}}{x} d x

Apply u-substitution

: \int 2 u^{9} d u

= \int 2 u^{9} d u

Take the constant out:

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

= 2 \cdot \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= 2 \cdot \frac{u ^{10}}{10}

Substitute back

u = 1 + x

= 2 \cdot \frac{( 1 + x ) ^{10}}{10}

Simplify

2 \cdot \frac{( 1 + x ) ^{10}}{10} : \frac{1}{5} (1 + x)^{10}

= \frac{1}{5} (1 + x)^{10}

Add a constant to the solution

= \frac{1}{5} (1 + x)^{10} + C

\int \frac{1}{x 361 x ^{2} - 361} d x

f (x) = 16 x, (16, 64)

\int \frac{1}{1 - 3 x} d x

\int x 3 2 x d x

f (t) = \frac{5 t ^{2} + t + 6}{t}

What is the integral of ((1+sqrt(x))^9)/(sqrt(x)) ?
The integral of ((1+sqrt(x))^9)/(sqrt(x)) is 1/5 (1+sqrt(x))^{10}+C