Question

score on last try: 3 of 4 pts. see details for more.
at least one scored part is incorrect. jump to first changable incorrect part.

next question get a similar question you can retry this question below

consider the indefinite integral $int x^{4}(x^{5}-2)^{34}dx.$
a) this can be transformed using the substitution
$u = x^5-2$
which gives $du = 5x^4dx$ (dont forget the differential $dx$ or $du$.)
c) performing the substitution in terms of $u$ gives the integral
$int \frac{1}{5}u^{34}$
d) evaluate the integral and simplify. your answer should be in terms of $x$, not $u$.
$\frac{(x^5-2)^{35}}{175}+c$
question help: video

Explanation:

Step1: Isolate $x^4 dx$ from $du$

From $du = 5x^4 dx$, solve for $x^4 dx$:
$\frac{1}{5}du = x^4 dx$

Step2: Substitute $u$ and $\frac{1}{5}du$

Replace $x^5-2$ with $u$ and $x^4 dx$ with $\frac{1}{5}du$ in the original integral:
$\int \frac{1}{5}u^{34} du$

Answer:

$\boldsymbol{\int \frac{1}{5}u^{34} du}$

(Note: The integral in part c) was marked incorrectly in the image; this is the correct substituted integral. The final antiderivative in part d) is already correct as $\frac{(x^5 - 2)^{35}}{175}+C$.)