What is the integral of (5x^4+2)(x^5+2x)^{2021} ?

The integral of (5x^4+2)(x^5+2x)^{2021} is ((x^5+2x)^{2022})/(2022)+C

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integral of (5x^4+2)(x^5+2x)^{2021}

\int (5 x^{4} + 2) (x^{5} + 2 x)^{2021} d x

\frac{( x ^{5} + 2 x ) ^{2022}}{2022} + C

Solution steps

\int (5 x^{4} + 2) (x^{5} + 2 x)^{2021} d x

Apply u-substitution

: \int u^{2021} d u

= \int u^{2021} d u

Apply the Power Rule

: \frac{u ^{2022}}{2022}

= \frac{u ^{2022}}{2022}

Substitute back

u = x^{5} + 2 x

= \frac{( x ^{5} + 2 x ) ^{2022}}{2022}

Add a constant to the solution

= \frac{( x ^{5} + 2 x ) ^{2022}}{2022} + C

8 sin^{4} (x)

\frac{d}{d x} (e^{x^{2} s i n (x)})

x \to 2 lim ([x (x - 2)])

f (x) = 11 - x^{2}

What is the integral of (5x^4+2)(x^5+2x)^{2021} ?
The integral of (5x^4+2)(x^5+2x)^{2021} is ((x^5+2x)^{2022})/(2022)+C