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Popular >

integral of 1/2 x^4

Solution

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

Solution

\frac{x ^{5}}{10} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{x ^{5}}{5}

Simplify

\frac{1}{2} \cdot \frac{x ^{5}}{5} : \frac{x ^{5}}{10}

= \frac{x ^{5}}{10}

Add a constant to the solution

= \frac{x ^{5}}{10} + C

Popular Examples

derivative of (440t)/((t^2+6)^3)derivative of

\frac{440 t}{( t ^{2} + 6 ) ^{3}}

f (x) = sin^{5} (3 x)

tangent of (7x)/(x+4)(3.3)tangent of

\frac{7 x}{x + 4} (3.3)

derivative of (x^3+x^6)

\frac{d}{d x} ((x^{3} + x)^{6})

derivative of ln(x+sqrt(x^2-10))derivative of

ln (x + x^{2} - 10)

Frequently Asked Questions (FAQ)

What is the integral of 1/2 x^4 ?
The integral of 1/2 x^4 is (x^5)/(10)+C