What is the integral of (xsqrt(x))/(1+x^2sqrt(x)) ?

The integral of (xsqrt(x))/(1+x^2sqrt(x)) is 2/5 ln|1+x^2sqrt(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (xsqrt(x))/(1+x^2sqrt(x))

\int \frac{x x}{1 + x ^{2} x} d x

\frac{2}{5} ln 1 + x^{2} x + C

Solution steps

\int \frac{x x}{1 + x ^{2} x} d x

Apply u-substitution

: \int \frac{2}{5 u} d u

= \int \frac{2}{5 u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{2}{5} ln ∣ u ∣

Substitute back

u = 1 + x^{2} x

= \frac{2}{5} ln 1 + x^{2} x

Add a constant to the solution

= \frac{2}{5} ln 1 + x^{2} x + C

\int \frac{2 x ^{2}}{8 + x ^{2}} d x

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

\int \frac{1 + cos ( 4 t )}{2} d t

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

cos (t)

What is the integral of (xsqrt(x))/(1+x^2sqrt(x)) ?
The integral of (xsqrt(x))/(1+x^2sqrt(x)) is 2/5 ln|1+x^2sqrt(x)|+C