What is the integral of (5.45)/((1+1.9x)^{0.9)} ?

The integral of (5.45)/((1+1.9x)^{0.9)} is 28.68421…(1+1.9x)^{0.1}+C

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integral of (5.45)/((1+1.9x)^{0.9)}

\int \frac{5.45}{( 1 + 1.9 x ) ^{0.9}} d x

28.68421 \dots (1 + 1.9 x)^{0.1} + C

Solution steps

\int \frac{5.45}{( 1 + 1.9 x ) ^{0.9}} d x

Take the constant out:

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

= 5.45 \cdot \int \frac{1}{( 1 + 1.9 x ) ^{0.9}} d x

Apply u-substitution

: \int \frac{1}{1.9 u ^{0.9}} d u

= 5.45 \cdot \int \frac{1}{1.9 u ^{0.9}} d u

Take the constant out:

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

= 5.45 \cdot \frac{1}{1.9} \cdot \int \frac{1}{u ^{0.9}} d u

Simplify

= 5.45 \cdot 0.52631 \dots \cdot \int \frac{1}{u ^{0.9}} d u

Apply the Power Rule

: 10 u^{0.1}

= 5.45 \cdot 0.52631 \dots \cdot 10 u^{0.1}

Substitute back

u = 1 + 1.9 x

= 5.45 \cdot 0.52631 \dots \cdot 10 (1 + 1.9 x)^{0.1}

Simplify

= 28.68421 \dots (1 + 1.9 x)^{0.1}

Add a constant to the solution

= 28.68421 \dots (1 + 1.9 x)^{0.1} + C

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What is the integral of (5.45)/((1+1.9x)^{0.9)} ?
The integral of (5.45)/((1+1.9x)^{0.9)} is 28.68421…(1+1.9x)^{0.1}+C