Evaluate ∫ e^sin x cos x dx.

Question 24

MediumOriginal question

Evaluate $\int e^{\sin x} \cos x\,dx$ .

2 e^{\sin x} + C

Correct answerYour answer

- e^{\sin x} + C

Correct answerYour answer

x e^{\sin x} \cos x + C

Correct answerYour answer

e^{\sin x} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

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

Worth noting

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

Ten questions from Indefinite Integrals, at your own pace.