`int x^3 (2 + x^4)^5 dx, u = 2 + x^4` Evaluate the integral by making the given substitution.

You need to evaluate the indefinite integral by performing the indicated substitution `u = 2+x^4` , such that:

`u = 2+x^4, => du = 4x^3 dx=> x^3dx = (du)/4`

`int x^3*(2+x^4)^5 dx = (1/4)*intu^5 du`

Using the formula `int u^n du = (u^(n+1))/(n+1) + c` yields

`(1/4)*int u^5 du = (1/4)(u^(5+1))/(5+1) + c`

`(1/4)*int u^5 du = (1/24)(u^6)+ c`

Replacing back  `2+x^4`   for u yields:

`int x^3*(2+x^4)^5 dx =(1/24)*(2+x^4)^6+ c`

Hence, evaluating the indefinite integral yields `int x^3*(2+x^4)^5 dx =((2+x^4)^6)/24+...

You need to evaluate the indefinite integral by performing the indicated substitution `u = 2+x^4` , such that:

`u = 2+x^4, => du = 4x^3 dx=> x^3dx = (du)/4`

`int x^3*(2+x^4)^5 dx = (1/4)*intu^5 du`

Using the formula `int u^n du = (u^(n+1))/(n+1) + c` yields

`(1/4)*int u^5 du = (1/4)(u^(5+1))/(5+1) + c`

`(1/4)*int u^5 du = (1/24)(u^6)+ c`

Replacing back  `2+x^4`   for u yields:

`int x^3*(2+x^4)^5 dx =(1/24)*(2+x^4)^6+ c`

Hence, evaluating the indefinite integral yields `int x^3*(2+x^4)^5 dx =((2+x^4)^6)/24+ c`