Evaluate ∫ 2 x (x^2 + 1)^4 dx.

Question 16

EasyOriginal question

Evaluate $\int 2 x \left(x^{2} + 1\right)^{4}\,dx$ .

\frac{2(x^2 + 1)^5}{5} + C

Correct answerYour answer

\frac{(x^2 + 1)^5}{5} + C

Correct answerYour answer

-\frac{(x^2 + 1)^5}{5} + C

Correct answerYour answer

2 x^{2} \left(x^{2} + 1\right)^{4} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Put $t = x^2 + 1$ ; then $dt$ is the rest of the integrand, up to a constant.
The integral becomes a standard form in $t$ ; putting $t = x^2 + 1$ back gives $\frac{(x^2 + 1)^5}{5} + C$ .
Check: differentiating the answer gives back the integrand.

Worth noting

Getting the constant from $dt$ wrong multiplies or divides the answer: check by differentiating.

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