What is the integral from 0 to 3 of m^2(4m^2+2)^3 ?

The integral from 0 to 3 of m^2(4m^2+2)^3 is 4sqrt(2)(-(181764sqrt(2))/(35)+26739sqrt(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3 of m^2(4m^2+2)^3

\int_{0}^{3} m^{2} (4 m^{2} + 2)^{3} d m

42 (- \frac{181764 2}{35} + 267392)

Decimal Notation

172365.94285 \dots

Solution steps

\int_{0}^{3} m^{2} (4 m^{2} + 2)^{3} d m

Apply Integral Substitution

= \int_{0}^{32} \frac{4 u ^{2} ( u ^{2} + 1 ) ^{3}}{2} d u

Take the constant out:

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

= \frac{4}{2} \cdot \int_{0}^{32} u^{2} (u^{2} + 1)^{3} d u

\frac{4}{2} = 22

= 22 \cdot \int_{0}^{32} u^{2} (u^{2} + 1)^{3} d u

Apply Integration By Parts

: [\frac{1}{3} (u^{3} (u^{2} + 1)^{3} - 3 \cdot \int 2 u^{4} (u^{2} + 1)^{2} d u)]_{0}^{32}

= 22 [\frac{1}{3} (u^{3} (u^{2} + 1)^{3} - 3 \cdot \int 2 u^{4} (u^{2} + 1)^{2} d u)]_{0}^{32}

\int 2 u^{4} (u^{2} + 1)^{2} d u = 2 (\frac{u ^{9}}{9} + \frac{2 u ^{7}}{7} + \frac{u ^{5}}{5})

= 22 [\frac{1}{3} (u^{3} (u^{2} + 1)^{3} - 3 \cdot 2 (\frac{u ^{9}}{9} + \frac{2 u ^{7}}{7} + \frac{u ^{5}}{5}))]_{0}^{32}

Simplify

22 [\frac{1}{3} (u^{3} (u^{2} + 1)^{3} - 3 \cdot 2 (\frac{u ^{9}}{9} + \frac{2 u ^{7}}{7} + \frac{u ^{5}}{5}))]_{0}^{32} : 22 [\frac{1}{3} (u^{3} (u^{2} + 1)^{3} - 6 (\frac{u ^{9}}{9} + \frac{2 u ^{7}}{7} + \frac{u ^{5}}{5}))]_{0}^{32}

= 22 [\frac{1}{3} (u^{3} (u^{2} + 1)^{3} - 6 (\frac{u ^{9}}{9} + \frac{2 u ^{7}}{7} + \frac{u ^{5}}{5}))]_{0}^{32}

Compute the boundaries:

2 (- \frac{181764 2}{35} + 267392)

= 22 \cdot 2 (- \frac{181764 2}{35} + 267392)

Simplify

= 42 (- \frac{181764 2}{35} + 267392)

\int_{- 1}^{1} (1 - x^{2}) cos (nπ x) d x

\int_{0}^{π} e^{s i n (x)} d x

\int_{- l n (2)}^{l n (2)} e^{x} d x

\int_{0}^{2} ∣ 3 x - 2 ∣ d x

\int_{- 1}^{0} 3 x^{2} e^{- x^{3} + 1} d x

What is the integral from 0 to 3 of m^2(4m^2+2)^3 ?
The integral from 0 to 3 of m^2(4m^2+2)^3 is 4sqrt(2)(-(181764sqrt(2))/(35)+26739sqrt(2))