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Popular >

integral of x^35x

Solution

\int x^{3} 5 x d x

Solution

x^{5} + C

Solution steps

\int x^{3} \cdot 5 x d x

Take the constant out:

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

= 5 \cdot \int x^{3} x d x

Simplify

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

= 5 \cdot \int x^{4} d x

Apply the Power Rule

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

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

Simplify

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

= x^{5}

Add a constant to the solution

= x^{5} + C

Popular Examples

limit as x approaches 0 of (cos(6x))/1

x \to 0 lim (\frac{cos ( 6 x )}{1})

limit as x approaches 3 of (2x-6)/(x-3)

x \to 3 lim (\frac{2 x - 6}{x - 3})

integral from 0 to pi of xsin(nx)

\int_{0}^{π} x sin (n x) d x

y^'=sqrt(y),y(0)=0

y^{^{'}} = y, y (0) = 0

y^{''}-2y^'-3y=e^{-x}

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{- x}

Frequently Asked Questions (FAQ)

What is the integral of x^35x ?
The integral of x^35x is x^5+C