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Popular >

integral of x^3Inx

Solution

\int x^{3} I n x d x

Solution

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

Solution steps

\int x^{3} I n x d x

Take the constant out:

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

= I n \cdot \int x x^{3} d x

Simplify

x x^{3} : x^{4}

= I n \cdot \int x^{4} d x

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of (1.05)/(1+100e^{-0.285t)}

\int \frac{1.05}{1 + 100 e ^{- 0.285 t}} d t

derivative of 3sin(x+4cos(x))

\frac{d}{d x} (3 sin (x) + 4 cos (x))

integral from 1 to 2 of (2x^3-4)

\int_{1}^{2} (2 x^{3} - 4) d x

derivative of f(x)=(1+6x^2)(x-x^2)derivative of

f (x) = (1 + 6 x^{2}) (x - x^{2})

sum from n=1 to infinity of (nx^n)/(n+1)

n = 1 \sum \infty \frac{n x ^{n}}{n + 1}

Frequently Asked Questions (FAQ)

What is the integral of x^3Inx ?
The integral of x^3Inx is (Inx^5)/5+C