What is the integral of (3x^2)/(sqrt(x^3+7)) ?

The integral of (3x^2)/(sqrt(x^3+7)) is 2sqrt(x^3+7)+C

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integral of (3x^2)/(sqrt(x^3+7))

\int \frac{3 x ^{2}}{x ^{3} + 7} d x

2 x^{3} + 7 + C

Solution steps

\int \frac{3 x ^{2}}{x ^{3} + 7} d x

Take the constant out:

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

= 3 \cdot \int \frac{x ^{2}}{x ^{3} + 7} d x

Apply u-substitution

: \int \frac{2}{3} d u

= 3 \cdot \int \frac{2}{3} d u

Integral of a constant:

\int a d x = a x

= 3 \cdot \frac{2}{3} u

Substitute back

u = x^{3} + 7

= 3 \cdot \frac{2}{3} x^{3} + 7

Simplify

3 \cdot \frac{2}{3} x^{3} + 7 : 2 x^{3} + 7

= 2 x^{3} + 7

Add a constant to the solution

= 2 x^{3} + 7 + C

\frac{d}{d x} (x y)

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- t} sin (t)

f^{^{'}} (x) = (\frac{1 - sec ( x )}{tan ( x )})

\frac{\partial}{\partial x} (1 - x^{2})

\frac{\partial}{\partial x} (r cos (t) sin (x))

What is the integral of (3x^2)/(sqrt(x^3+7)) ?
The integral of (3x^2)/(sqrt(x^3+7)) is 2sqrt(x^3+7)+C