What is the integral of 2x(\sqrt[3]{(x+3)}) ?

The integral of 2x(\sqrt[3]{(x+3)}) is 2(3/7 (x+3)^{7/3}-9/4 (x+3)^{4/3})+C

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integral of 2x(\sqrt[3]{(x+3)})

2 (\frac{3}{7} (x + 3)^{\frac{7}{3}} - \frac{9}{4} (x + 3)^{\frac{4}{3}}) + C

Solution steps

Take the constant out:

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

Apply u-substitution

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int u^{\frac{4}{3}} d u = \frac{3}{7} u^{\frac{7}{3}}

= 2 (\frac{3}{7} u^{\frac{7}{3}} - \frac{9}{4} u^{\frac{4}{3}})

Substitute back

u = x + 3

= 2 (\frac{3}{7} (x + 3)^{\frac{7}{3}} - \frac{9}{4} (x + 3)^{\frac{4}{3}})

Add a constant to the solution

= 2 (\frac{3}{7} (x + 3)^{\frac{7}{3}} - \frac{9}{4} (x + 3)^{\frac{4}{3}}) + C

5 y^{^{''}} + 60 y = 0

\int_{0}^{\frac{1}{2}} \frac{4}{1 + 4 t ^{2}} d t

ln (x^{2} - 8 x + 1)

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

x \to - 1 lim (x (- 1))

What is the integral of 2x(\sqrt[3]{(x+3)}) ?
The integral of 2x(\sqrt[3]{(x+3)}) is 2(3/7 (x+3)^{7/3}-9/4 (x+3)^{4/3})+C