What is the integral of x^2(x^3-11)^6 ?

The integral of x^2(x^3-11)^6 is 1/21 (x^3-11)^7+C

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integral of x^2(x^3-11)^6

\int x^{2} (x^{3} - 11)^{6} d x

\frac{1}{21} (x^{3} - 11)^{7} + C

Solution steps

\int x^{2} (x^{3} - 11)^{6} d x

Apply u-substitution

: \int \frac{u ^{6}}{3} d u

= \int \frac{u ^{6}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= \frac{1}{3} \cdot \frac{u ^{7}}{7}

Substitute back

u = x^{3} - 11

= \frac{1}{3} \cdot \frac{( x ^{3} - 11 ) ^{7}}{7}

Simplify

\frac{1}{3} \cdot \frac{( x ^{3} - 11 ) ^{7}}{7} : \frac{1}{21} (x^{3} - 11)^{7}

= \frac{1}{21} (x^{3} - 11)^{7}

Add a constant to the solution

= \frac{1}{21} (x^{3} - 11)^{7} + C

n = 1 \sum \infty \frac{1}{1 + 2 ^{n}}

ln (1 + x^{5})

\int x^{2} 11 + x^{3} d x

f (x) = tan (3 x)

\frac{d}{d x} (- 0.9 x^{2} + 1.7 x + 2.5)

What is the integral of x^2(x^3-11)^6 ?
The integral of x^2(x^3-11)^6 is 1/21 (x^3-11)^7+C