What is the integral of ((e^x)/3+xsqrt(2x)) ?

The integral of ((e^x)/3+xsqrt(2x)) is 1/3 e^x+1/(sqrt(2))x^2sqrt(x)-1/(5sqrt(2))x^{5/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((e^x)/3+xsqrt(2x))

\int (\frac{e ^{x}}{3} + x 2 x) d x

\frac{1}{3} e^{x} + \frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}} + C

Solution steps

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

Apply the Sum Rule:

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

= \int \frac{e ^{x}}{3} d x + \int x 2 x d x

\int \frac{e ^{x}}{3} d x = \frac{1}{3} e^{x}

\int x 2 x d x = \frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}

= \frac{1}{3} e^{x} + \frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{1}{3} e^{x} + \frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}} + C

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

\int tanh^{2} (2 x) d x

\int \frac{1}{2} e^{- x} d x

\int x 4 - 9 x^{2} d x

What is the integral of ((e^x)/3+xsqrt(2x)) ?
The integral of ((e^x)/3+xsqrt(2x)) is 1/3 e^x+1/(sqrt(2))x^2sqrt(x)-1/(5sqrt(2))x^{5/2}+C