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

The integral of x^5(x^6+5)^5 is 1/36 (x^6+5)^6+C

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

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

\frac{1}{36} (x^{6} + 5)^{6} + C

Solution steps

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

Apply u-substitution

: \int \frac{u ^{5}}{6} d u

= \int \frac{u ^{5}}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{6} \cdot \frac{u ^{6}}{6}

Substitute back

u = x^{6} + 5

= \frac{1}{6} \cdot \frac{( x ^{6} + 5 ) ^{6}}{6}

Simplify

\frac{1}{6} \cdot \frac{( x ^{6} + 5 ) ^{6}}{6} : \frac{1}{36} (x^{6} + 5)^{6}

= \frac{1}{36} (x^{6} + 5)^{6}

Add a constant to the solution

= \frac{1}{36} (x^{6} + 5)^{6} + C

ln (x^{2} - 1)

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

\int \frac{x ^{3}}{x ^{4} + 1} d x

x \to 0 lim (\frac{tan ( x )}{5 x})

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

What is the integral of x^5(x^6+5)^5 ?
The integral of x^5(x^6+5)^5 is 1/36 (x^6+5)^6+C