What is the integral of x^3(1+x^4)^4 ?

The integral of x^3(1+x^4)^4 is 1/20 (1+x^4)^5+C

integral of x^3(1+x^4)^4

\int x^{3} (1 + x^{4})^{4} d x

\frac{1}{20} (1 + x^{4})^{5} + C

Solution steps

\int x^{3} (1 + x^{4})^{4} d x

Apply u-substitution

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

Apply the Power Rule

= \frac{1}{4} \cdot \frac{u ^{5}}{5}

Substitute back

u = 1 + x^{4}

= \frac{1}{4} \cdot \frac{( 1 + x ^{4} ) ^{5}}{5}

Simplify

\frac{1}{4} \cdot \frac{( 1 + x ^{4} ) ^{5}}{5} : \frac{1}{20} (1 + x^{4})^{5}

= \frac{1}{20} (1 + x^{4})^{5}

Add a constant to the solution

= \frac{1}{20} (1 + x^{4})^{5} + C

\int x sin (m x) d x

\int (4 - 16 x) sin (4 x) d x

\int \frac{1}{12 x - 1} d x

\int \frac{x ^{2}}{( 9 + x ^{2} ) ^{\frac{3}{2}}} d x

\int 24 x^{2} arctan (2 x^{3}) d x

What is the integral of x^3(1+x^4)^4 ?
The integral of x^3(1+x^4)^4 is 1/20 (1+x^4)^5+C