What is the integral of (x^3+3x)^{32}(3x^2+3) ?

The integral of (x^3+3x)^{32}(3x^2+3) is ((x^3+3x)^{33})/(33)+C

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integral of (x^3+3x)^{32}(3x^2+3)

\int (x^{3} + 3 x)^{32} (3 x^{2} + 3) d x

\frac{( x ^{3} + 3 x ) ^{33}}{33} + C

Solution steps

\int (x^{3} + 3 x)^{32} (3 x^{2} + 3) d x

Apply u-substitution

= \int u^{32} d u

Apply the Power Rule

= \frac{u ^{33}}{33}

Substitute back

u = x^{3} + 3 x

= \frac{( x ^{3} + 3 x ) ^{33}}{33}

Add a constant to the solution

= \frac{( x ^{3} + 3 x ) ^{33}}{33} + C

x \to \infty lim (1 + \frac{1}{x})

x x^{2} + 5

n = 2 \sum \infty \frac{1}{n}

\frac{d}{d x} (x^{- \frac{1}{5}})

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

What is the integral of (x^3+3x)^{32}(3x^2+3) ?
The integral of (x^3+3x)^{32}(3x^2+3) is ((x^3+3x)^{33})/(33)+C