What is the integral of yln(x)+xln(y)+z^2 ?

The integral of yln(x)+xln(y)+z^2 is (z^3)/3+ln(y)xz+ln(x)yz+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of yln(x)+xln(y)+z^2

\int y ln (x) + x ln (y) + z^{2} d z

\frac{z ^{3}}{3} + ln (y) x z + ln (x) yz + C

Solution steps

\int y ln (x) + x ln (y) + z^{2} d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int z^{2} d z + \int ln (y) x d z + \int ln (x) y d z

\int z^{2} d z = \frac{z ^{3}}{3}

\int ln (y) x d z = ln (y) x z

\int ln (x) y d z = ln (x) yz

= \frac{z ^{3}}{3} + ln (y) x z + ln (x) yz

Add a constant to the solution

= \frac{z ^{3}}{3} + ln (y) x z + ln (x) yz + C

\int sin (32 x) sin (cos (32 x)) d x

\int \frac{3}{x} + x^{2} - x^{3} d x

\int 2 x y \cdot cos (x^{2} y) d x

\int (3 x - x) d x

\int 2 t^{- 8} d t

What is the integral of yln(x)+xln(y)+z^2 ?
The integral of yln(x)+xln(y)+z^2 is (z^3)/3+ln(y)xz+ln(x)yz+C