What is the integral of ((sqrt(x)+7)^5)/(sqrt(x)) ?

The integral of ((sqrt(x)+7)^5)/(sqrt(x)) is 1/3 (sqrt(x)+7)^6+C

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integral of ((sqrt(x)+7)^5)/(sqrt(x))

\int \frac{( x + 7 ) ^{5}}{x} d x

\frac{1}{3} (x + 7)^{6} + C

Solution steps

\int \frac{( x + 7 ) ^{5}}{x} d x

Apply u-substitution

: \int 2 u^{5} d u

= \int 2 u^{5} d u

Take the constant out:

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

= 2 \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= 2 \cdot \frac{u ^{6}}{6}

Substitute back

u = x + 7

= 2 \cdot \frac{( x + 7 ) ^{6}}{6}

Simplify

2 \cdot \frac{( x + 7 ) ^{6}}{6} : \frac{1}{3} (x + 7)^{6}

= \frac{1}{3} (x + 7)^{6}

Add a constant to the solution

= \frac{1}{3} (x + 7)^{6} + C

\frac{d y}{d x} = \frac{- y ^{2}}{1 + y ^{2}} \cdot e^{- x}

\frac{\partial}{\partial z} ((x + z) e^{x - y})

\int \frac{1}{9 e ^{- 2 x} + e ^{2 x}} d x

\frac{d}{d x} (ln (sinh (4 x)))

y^{^{'}} + x^{- 1} y = \frac{2}{3} x^{4} y^{4}

What is the integral of ((sqrt(x)+7)^5)/(sqrt(x)) ?
The integral of ((sqrt(x)+7)^5)/(sqrt(x)) is 1/3 (sqrt(x)+7)^6+C