What is the integral of (8t^3)/(sqrt(0.2t^4+8000)) ?

The integral of (8t^3)/(sqrt(0.2t^4+8000)) is 20sqrt(0.2t^4+8000)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (8t^3)/(sqrt(0.2t^4+8000))

\int \frac{8 t ^{3}}{0.2 t ^{4} + 8000} d t

20 0.2 t^{4} + 8000 + C

Solution steps

\int \frac{8 t ^{3}}{0.2 t ^{4} + 8000} d t

Take the constant out:

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

= 8 \cdot \int \frac{t ^{3}}{0.2 t ^{4} + 8000} d t

Apply u-substitution

: \int \frac{1}{0.8 u} d u

= 8 \cdot \int \frac{1}{0.8 u} d u

Take the constant out:

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

= 8 \cdot \frac{1}{0.8} \cdot \int \frac{1}{u} d u

Simplify

= 8 \cdot 1.25 \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 8 \cdot 1.25 \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 0.2 t^{4} + 8000

= 8 \cdot 1.25 \cdot 2 (0.2 t^{4} + 8000)^{\frac{1}{2}}

Simplify

8 \cdot 1.25 \cdot 2 (0.2 t^{4} + 8000)^{\frac{1}{2}} : 20 0.2 t^{4} + 8000

= 20 0.2 t^{4} + 8000

Add a constant to the solution

= 20 0.2 t^{4} + 8000 + C

\int t^{2} (1 + 2 t^{3})^{- \frac{2}{3}} d t

\int (5 x^{4} - 8 x^{3} + 6 x - 3) d x

\int \frac{1}{x \cdot x ^{2} - 4} d x

\int \frac{w ^{3}}{w ^{4} - 5} d w

\int \frac{4 x - 5}{x ^{2} - 4 x + 8} d x

What is the integral of (8t^3)/(sqrt(0.2t^4+8000)) ?
The integral of (8t^3)/(sqrt(0.2t^4+8000)) is 20sqrt(0.2t^4+8000)+C