What is the integral of x^3in(3x) ?

The integral of x^3in(3x) is (3inx^5)/5+C

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integral of x^3in(3x)

\int x^{3} in (3 x) d x

\frac{3 in x ^{5}}{5} + C

Solution steps

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

Take the constant out:

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

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

Simplify

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

= in \cdot 3 \cdot \int x^{4} d x

Apply the Power Rule

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

= in \cdot 3 \cdot \frac{x ^{5}}{5}

Multiply fractions:

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

= \frac{3 in x ^{5}}{5}

Add a constant to the solution

= \frac{3 in x ^{5}}{5} + C

\frac{d}{d y} (cos (x^{2} y))

n = 2 \sum \infty \frac{ln ^{2} ( n )}{n}

\int_{0}^{x} \frac{2}{1 + t} d t

\frac{d}{d x} (cos^{3} (5 x + 1))

y^{^{''}} + 4 y = - 6, y (\frac{π}{8}) = - 12, y^{^{'}} (\frac{π}{8}) = 2