What is the integral of x/(x^2+2)7^{ln(x^2+2)} ?

The integral of x/(x^2+2)7^{ln(x^2+2)} is (7^{ln(x^2+2)})/(2ln(7))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/(x^2+2)7^{ln(x^2+2)}

\int \frac{x}{x ^{2} + 2} 7^{l n (x^{2} + 2)} d x

\frac{7 ^{l n (x^{2} + 2)}}{2 ln ( 7 )} + C

Solution steps

\int \frac{x}{x ^{2} + 2} \cdot 7^{l n (x^{2} + 2)} d x

Apply u-substitution

: \int \frac{7 ^{l n (u)}}{2 u} d u

= \int \frac{7 ^{l n (u)}}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{7 ^{l n (u)}}{u} d u

Apply u-substitution

: \int 7^{v} d v

= \frac{1}{2} \cdot \int 7^{v} d v

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

= \frac{1}{2} \cdot \frac{7 ^{v}}{ln ( 7 )}

Substitute back

= \frac{1}{2} \cdot \frac{7 ^{l n (x^{2} + 2)}}{ln ( 7 )}

Simplify

\frac{1}{2} \cdot \frac{7 ^{l n (x^{2} + 2)}}{ln ( 7 )} : \frac{7 ^{l n (x^{2} + 2)}}{2 ln ( 7 )}

= \frac{7 ^{l n (x^{2} + 2)}}{2 ln ( 7 )}

Add a constant to the solution

= \frac{7 ^{l n (x^{2} + 2)}}{2 ln ( 7 )} + C

\int \frac{x}{( 5 x ^{2} + 1 ) ^{2}} d x

\int \frac{sec ^{4} ( x )}{tan ^{4} ( x )} d x

\int sin (I n x) d x

\int cos (x) [sin (x) + 1]^{3} d x

\int \frac{x}{1 + x ^{6}} d x

What is the integral of x/(x^2+2)7^{ln(x^2+2)} ?
The integral of x/(x^2+2)7^{ln(x^2+2)} is (7^{ln(x^2+2)})/(2ln(7))+C