What is the integral of 2x(x^2+3)^{20} ?

The integral of 2x(x^2+3)^{20} is 1/21 (x^2+3)^{21}+C

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integral of 2x(x^2+3)^{20}

\int 2 x (x^{2} + 3)^{20} d x

\frac{1}{21} (x^{2} + 3)^{21} + C

Solution steps

\int 2 x (x^{2} + 3)^{20} d x

Take the constant out:

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

= 2 \cdot \int x (x^{2} + 3)^{20} d x

Apply u-substitution

= 2 \cdot \int \frac{u ^{20}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{20} d u

Apply the Power Rule

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{21}}{21}

Substitute back

u = x^{2} + 3

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{21}}{21}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{21}}{21} : \frac{1}{21} (x^{2} + 3)^{21}

= \frac{1}{21} (x^{2} + 3)^{21}

Add a constant to the solution

= \frac{1}{21} (x^{2} + 3)^{21} + C

\frac{d}{d x} (0.8 x^{2} - 3 x + 5 x^{0.2} - 5200)

d er i v a t i v e - \frac{3}{( 3 x + 1 ) ^{2}}

\frac{d y}{d x} = \frac{x ^{2} + y ^{2}}{2 y}

x \to 3 lim (\frac{1}{x} - \frac{1}{3})

(y x^{2} - y) d y = tan^{- 1} (x) d x

What is the integral of 2x(x^2+3)^{20} ?
The integral of 2x(x^2+3)^{20} is 1/21 (x^2+3)^{21}+C