What is the integral of x^3(x^4+16)^6 ?

The integral of x^3(x^4+16)^6 is 1/28 (x^4+16)^7+C

Popular >

integral of x^3(x^4+16)^6

\int x^{3} (x^{4} + 16)^{6} d x

\frac{1}{28} (x^{4} + 16)^{7} + C

Solution steps

\int x^{3} (x^{4} + 16)^{6} d x

Apply u-substitution

: \int \frac{u ^{6}}{4} d u

= \int \frac{u ^{6}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int u^{6} d u

Apply the Power Rule

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

= \frac{1}{4} \cdot \frac{u ^{7}}{7}

Substitute back

u = x^{4} + 16

= \frac{1}{4} \cdot \frac{( x ^{4} + 16 ) ^{7}}{7}

Simplify

\frac{1}{4} \cdot \frac{( x ^{4} + 16 ) ^{7}}{7} : \frac{1}{28} (x^{4} + 16)^{7}

= \frac{1}{28} (x^{4} + 16)^{7}

Add a constant to the solution

= \frac{1}{28} (x^{4} + 16)^{7} + C

\int \frac{1}{2 x ^{2} - 6 x + 5} d x

\int t sec^{2} (t^{2}) tan^{4} (t^{2}) d t

\int \frac{1}{6 x ^{2} + 3 x + 1} d x

\int p (p + 7)^{5} d p

\int \frac{v}{v ^{2} - 16} d v

What is the integral of x^3(x^4+16)^6 ?
The integral of x^3(x^4+16)^6 is 1/28 (x^4+16)^7+C