What is the integral of 3(5^{1-2x}) ?

The integral of 3(5^{1-2x}) is -(3*5^{1-2x})/(2ln(5))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3(5^{1-2x})

\int 3 (5^{1 - 2 x}) d x

- \frac{3 \cdot 5 ^{1 - 2 x}}{2 ln ( 5 )} + C

Solution steps

\int 3 \cdot 5^{1 - 2 x} d x

Take the constant out:

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

= 3 \cdot \int 5^{1 - 2 x} d x

Apply u-substitution

: \int - \frac{1}{2} \cdot 5^{u} d u

= 3 \cdot \int - \frac{1}{2} \cdot 5^{u} d u

Take the constant out:

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

= 3 (- \frac{1}{2} \cdot \int 5^{u} d u)

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 3 (- \frac{1}{2} \cdot \frac{5 ^{u}}{ln ( 5 )})

Substitute back

u = 1 - 2 x

= 3 (- \frac{1}{2} \cdot \frac{5 ^{1 - 2 x}}{ln ( 5 )})

Simplify

3 (- \frac{1}{2} \cdot \frac{5 ^{1 - 2 x}}{ln ( 5 )}) : - \frac{3 \cdot 5 ^{1 - 2 x}}{2 ln ( 5 )}

= - \frac{3 \cdot 5 ^{1 - 2 x}}{2 ln ( 5 )}

Add a constant to the solution

= - \frac{3 \cdot 5 ^{1 - 2 x}}{2 ln ( 5 )} + C

\frac{d}{d x} (40 x)

x \to - 2 lim (3 x - 1)

\int \frac{ln ( x ^{2} + 1 )}{x ^{3}} d x

\frac{\partial}{\partial x} (x^{0.25} Y (x)^{0.5})

2 x^{2} - x - 3

What is the integral of 3(5^{1-2x}) ?
The integral of 3(5^{1-2x}) is -(3*5^{1-2x})/(2ln(5))+C