What is the integral of (6x^5+7)sqrt(x^6+7x) ?

The integral of (6x^5+7)sqrt(x^6+7x) is 2/3 (x^6+7x)^{3/2}+C

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integral of (6x^5+7)sqrt(x^6+7x)

\int (6 x^{5} + 7) x^{6} + 7 x d x

\frac{2}{3} (x^{6} + 7 x)^{\frac{3}{2}} + C

Solution steps

\int (6 x^{5} + 7) x^{6} + 7 x d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

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

Substitute back

u = x^{6} + 7 x

= \frac{2}{3} (x^{6} + 7 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x^{6} + 7 x)^{\frac{3}{2}} + C

lo g_{e} (sec (\frac{1}{5 x}))

\frac{5}{s ^{2}}

\int e^{2 t} cos (e^{t}) d t

x \to + 3 + lim (\frac{x + 9}{x - 3})

\frac{d}{d x} (3 tan^{2} (x))

What is the integral of (6x^5+7)sqrt(x^6+7x) ?
The integral of (6x^5+7)sqrt(x^6+7x) is 2/3 (x^6+7x)^{3/2}+C