What is the integral of (5.4518)/((1+1.09x)^{0.9)} ?

The integral of (5.4518)/((1+1.09x)^{0.9)} is 50.01651…(1+1.09x)^{0.1}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5.4518)/((1+1.09x)^{0.9)}

\int \frac{5.4518}{( 1 + 1.09 x ) ^{0.9}} d x

50.01651 \dots (1 + 1.09 x)^{0.1} + C

Solution steps

\int \frac{5.4518}{( 1 + 1.09 x ) ^{0.9}} d x

Take the constant out:

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

= 5.4518 \cdot \int \frac{1}{( 1 + 1.09 x ) ^{0.9}} d x

Apply u-substitution

: \int \frac{1}{1.09 u ^{0.9}} d u

= 5.4518 \cdot \int \frac{1}{1.09 u ^{0.9}} d u

Take the constant out:

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

= 5.4518 \cdot \frac{1}{1.09} \cdot \int \frac{1}{u ^{0.9}} d u

Simplify

= 5.4518 \cdot 0.91743 \dots \cdot \int \frac{1}{u ^{0.9}} d u

Apply the Power Rule

: 10 u^{0.1}

= 5.4518 \cdot 0.91743 \dots \cdot 10 u^{0.1}

Substitute back

u = 1 + 1.09 x

= 5.4518 \cdot 0.91743 \dots \cdot 10 (1 + 1.09 x)^{0.1}

Simplify

= 50.01651 \dots (1 + 1.09 x)^{0.1}

Add a constant to the solution

= 50.01651 \dots (1 + 1.09 x)^{0.1} + C

\int (2 x + 1)^{35} d x

\int \frac{y ^{2} - 5 y + 6}{y ^{2} + 4} d y

\int (\frac{1}{x ^{3} + x}) d x

\int 0.024 (0.03 x^{2} - 2 x) + 130 d x

\int sec^{\frac{5}{2}} (x) tan (x) d x

What is the integral of (5.4518)/((1+1.09x)^{0.9)} ?
The integral of (5.4518)/((1+1.09x)^{0.9)} is 50.01651…(1+1.09x)^{0.1}+C