What is the integral of (5.4145)/(sqrt(1+0.91x)) ?

The integral of (5.4145)/(sqrt(1+0.91x)) is 11.9sqrt(1+0.91x)+C

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integral of (5.4145)/(sqrt(1+0.91x))

\int \frac{5.4145}{1 + 0.91 x} d x

11.9 1 + 0.91 x + C

Solution steps

\int \frac{5.4145}{1 + 0.91 x} d x

Take the constant out:

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

= 5.4145 \cdot \int \frac{1}{1 + 0.91 x} d x

Apply u-substitution

: \int \frac{1}{0.91 u} d u

= 5.4145 \cdot \int \frac{1}{0.91 u} d u

Take the constant out:

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

= 5.4145 \cdot \frac{1}{0.91} \cdot \int \frac{1}{u} d u

Simplify

= 5.4145 \cdot 1.09890 \dots \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 5.4145 \cdot 1.09890 \dots \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 1 + 0.91 x

= 5.4145 \cdot 1.09890 \dots \cdot 2 (1 + 0.91 x)^{\frac{1}{2}}

Simplify

5.4145 \cdot 1.09890 \dots \cdot 2 (1 + 0.91 x)^{\frac{1}{2}} : 11.9 1 + 0.91 x

= 11.9 1 + 0.91 x

Add a constant to the solution

= 11.9 1 + 0.91 x + C

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What is the integral of (5.4145)/(sqrt(1+0.91x)) ?
The integral of (5.4145)/(sqrt(1+0.91x)) is 11.9sqrt(1+0.91x)+C