What is the integral of x^2sqrt(x^{3+1)} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2sqrt(x^{3+1)}

\int x^{2} x^{3 + 1} d x

\frac{x ^{5}}{5} + C

Solution steps

\int x^{2} x^{3 + 1} d x

x^{3 + 1} = x^{2},

assuming

x \geq 0

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

Simplify

x^{2} x^{2} : x^{4}

= \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{5}}{5} + C

x \to - 1 lim (\frac{x - 1}{x ^{1} - 1})

\int \frac{x ^{3} + x - 2}{x ^{4} + 2 x ^{3} + 3 x ^{2}} d x

(x^{2} + y^{2})^{2} = 4 x^{2} y, (- 1, 1)

\int_{1}^{10} \frac{x ^{2} - 1}{x} d x

\frac{d}{d x} (ln (2 π x^{2}))

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