What is the integral of 5/(sqrt(x)(7+5\sqrt{x))^6} ?

The integral of 5/(sqrt(x)(7+5\sqrt{x))^6} is -2/(5(7+5sqrt(x))^5)+C

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integral of 5/(sqrt(x)(7+5\sqrt{x))^6}

\int \frac{5}{x ( 7 + 5 x ) ^{6}} d x

- \frac{2}{5 ( 7 + 5 x ) ^{5}} + C

Solution steps

\int \frac{5}{x ( 7 + 5 x ) ^{6}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{x ( 7 + 5 x ) ^{6}} d x

Apply u-substitution

: \int \frac{2}{5 u ^{6}} d u

= 5 \cdot \int \frac{2}{5 u ^{6}} d u

Take the constant out:

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

= 5 \cdot \frac{2}{5} \cdot \int \frac{1}{u ^{6}} d u

Apply the Power Rule

: - \frac{1}{5 u ^{5}}

= 5 \cdot \frac{2}{5} (- \frac{1}{5 u ^{5}})

Substitute back

u = 7 + 5 x

= 5 \cdot \frac{2}{5} (- \frac{1}{5 ( 7 + 5 x ) ^{5}})

Simplify

5 \cdot \frac{2}{5} (- \frac{1}{5 ( 7 + 5 x ) ^{5}}) : - \frac{2}{5 ( 7 + 5 x ) ^{5}}

= - \frac{2}{5 ( 7 + 5 x ) ^{5}}

Add a constant to the solution

= - \frac{2}{5 ( 7 + 5 x ) ^{5}} + C

f (t) = tan (sec (cos (t)))

x \to 1 + lim (x)

x \to 5 lim (76)

\frac{d y}{d x} = x + y, y (0) = 1

\int_{- 5}^{7} (\frac{x}{2} + 7) d x

What is the integral of 5/(sqrt(x)(7+5\sqrt{x))^6} ?
The integral of 5/(sqrt(x)(7+5\sqrt{x))^6} is -2/(5(7+5sqrt(x))^5)+C