What is the integral of (x^3)/(324) ?

The integral of (x^3)/(324) is (x^4)/(1296)+C

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integral of (x^3)/(324)

\int \frac{x ^{3}}{324} d x

\frac{x ^{4}}{1296} + C

Solution steps

\int \frac{x ^{3}}{324} d x

Take the constant out:

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

= \frac{1}{324} \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= \frac{1}{324} \cdot \frac{x ^{4}}{4}

Simplify

\frac{1}{324} \cdot \frac{x ^{4}}{4} : \frac{x ^{4}}{1296}

= \frac{x ^{4}}{1296}

Add a constant to the solution

= \frac{x ^{4}}{1296} + C

\int_{0}^{\infty} \frac{x}{1 + x ^{3}} d x

x \to 4 lim (x^{2})

9 y^{^{''}} + 4 y = 0

y^{^{''}} + 4 y = x^{2} + 3 e^{x}, y (0) = 0, y^{^{'}} (0) = 2

2 - 4 x

What is the integral of (x^3)/(324) ?
The integral of (x^3)/(324) is (x^4)/(1296)+C