What is the integral of 2^x2^{2^x} ?

The integral of 2^x2^{2^x} is 1/(ln^2(2))*2^{2^x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2^x2^{2^x}

\int 2^{x} 2^{2^{x}} d x

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

Solution steps

\int 2^{x} \cdot 2^{2^{x}} d x

Apply u-substitution

: \int \frac{2 ^{u}}{ln ( 2 )} d u

= \int \frac{2 ^{u}}{ln ( 2 )} d u

Take the constant out:

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

= \frac{1}{ln ( 2 )} \cdot \int 2^{u} d u

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

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

Substitute back

u = 2^{x}

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

Simplify

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

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

Add a constant to the solution

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

\int 3 x^{5} + x^{2} ln (x) d x

\int \frac{X ^{2}}{X ( X ^{2} - 9 )} d X

\int csc^{2} (6 x) cot (6 x) d x

\int e^{5 x} (e^{5 x} + 2)^{7} d x

\int \frac{x ^{2}}{x ^{2} + 6} d x

What is the integral of 2^x2^{2^x} ?
The integral of 2^x2^{2^x} is 1/(ln^2(2))*2^{2^x}+C