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Popular >

integral of v(u+v^2)^4

Solution

\int v (u + v^{2})^{4} d u

Solution

\frac{v ( v ^{2} + u ) ^{5}}{5} + C

Solution steps

\int v (u + v^{2})^{4} d u

Take the constant out:

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

= v \cdot \int (v^{2} + u)^{4} d u

Apply u-substitution

: \int w^{4} d w

= v \cdot \int w^{4} d w

Apply the Power Rule

: \frac{w ^{5}}{5}

= v \frac{w ^{5}}{5}

Substitute back

w = v^{2} + u

= v \frac{( v ^{2} + u ) ^{5}}{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{v ( v ^{2} + u ) ^{5}}{5}

Add a constant to the solution

= \frac{v ( v ^{2} + u ) ^{5}}{5} + C

Popular Examples

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\int sin (θ) d θ

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\frac{d}{d x} (6 x + 7 x)

(\partial)/(\partial x)(-2sqrt(x^2+y^2))

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\frac{d}{d x} (x^{- \frac{4}{3}})

y^'+ky=e^{-7kx}

y^{^{'}} + k y = e^{- 7 k x}

Frequently Asked Questions (FAQ)

What is the integral of v(u+v^2)^4 ?
The integral of v(u+v^2)^4 is (v(v^2+u)^5)/5+C