Question

Evaluate the indefinite integral

x^3sqrt(12+x^4)dx

Answer 1

let u=12+x^4
du=4x^3 dx

Answer 2

you got the answer i was confused on what to integrate first the sqrt(u) or just (u) itself because i kept on getting the wrong answer

Answer 3

if du=4x^3 dx
then du/4=x^3 dx right?

Answer 4

\[\int\limits_{}^{}x^3 \sqrt{12+x^4} dx =\int\limits_{}^{} \sqrt{12+x^4} x^3 dx\]
\[=\int\limits_{}^{}\sqrt{u} \frac{du}{4}\]

Answer 5

\[=\frac{1}{4}\int\limits_{}^{}\sqrt{u} du=\frac{1}{4}\int\limits_{}^{}u^\frac{1}{2} du\]

Answer 6

yeah i got eh right answer in the end but this step by step gives a better understanding too

Answer 7

\[=\frac{1}{4} \cdot \frac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1}+C\]
replace u with 12+x^4