What is the integral of 4/(7^{ln(x))} ?

The integral of 4/(7^{ln(x))} is (4x)/((1-ln(7))*7^{ln(x))}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(7^{ln(x))}

\int \frac{4}{7 ^{l n (x)}} d x

\frac{4 x}{( 1 - ln ( 7 ) ) \cdot 7 ^{l n (x)}} + C

Solution steps

\int \frac{4}{7 ^{l n (x)}} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{7 ^{l n (x)}} d x

Apply u-substitution

: \int (\frac{e}{7})^{u} d u

= 4 \cdot \int (\frac{e}{7})^{u} d u

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

= 4 \cdot \frac{( \frac{e}{7} ) ^{u}}{ln ( \frac{e}{7} )}

Substitute back

u = ln (x)

= 4 \cdot \frac{( \frac{e}{7} ) ^{l n (x)}}{ln ( \frac{e}{7} )}

Simplify

4 \cdot \frac{( \frac{e}{7} ) ^{l n (x)}}{ln ( \frac{e}{7} )} : \frac{4 x}{( 1 - ln ( 7 ) ) \cdot 7 ^{l n (x)}}

= \frac{4 x}{( 1 - ln ( 7 ) ) \cdot 7 ^{l n (x)}}

Add a constant to the solution

= \frac{4 x}{( 1 - ln ( 7 ) ) \cdot 7 ^{l n (x)}} + C

x \to 0 + lim (ln (x^{x}))

\int cos (x) csc (x) d x

\frac{d}{d x} (x^{2} \cdot f (x))

\frac{d}{d x} (e^{- arcsinh (\frac{x}{2})})

\frac{x}{6 x - 6}

What is the integral of 4/(7^{ln(x))} ?
The integral of 4/(7^{ln(x))} is (4x)/((1-ln(7))*7^{ln(x))}+C