Evaluate ∫ (sin x + cos x)^2 dx.

Indefinite Integrals · Question 39 of 90

Question 39

MediumOriginal question

Evaluate $\int (\sin x + \cos x)^{2}\,dx$ .

\frac{(\sin x + \cos x)^{3}}{3} + C

Correct answerYour answer

x - \frac{\cos 2x}{2} + C

Correct answerYour answer

x + \frac{\cos 2x}{2} + C

Correct answerYour answer

x - \cos 2x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$(\sin x + \cos x)^{2} = \sin^{2} x + \cos^{2} x + 2\sin x\cos x = 1 + \sin 2x$ .
$\int (1 + \sin 2x)\,dx = x - \frac{\cos 2x}{2} + C$ .

Worth noting

Raising the bracket to the power 3 treats it like $x$ ; its derivative brings an extra factor $\cos x - \sin x$ .

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.