Question Bank : : Integration by Parts

. Find \( \int x e^x d x\)
Answer : \( x e^x-e^x+c\)
. \( \) .

. Find \( \int x \sin x d x\)
Answer : \( -x \cos x+\sin x+c\)
. \( \) .

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Question No: 3 [Maximum Mark: 7] (Do not use GDC)

. Find \( \int x \sec ^2 x d x\)
Answer : \( x \tan x+\ln \cos x+c\)
. \( \) .

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Question No: 4 [Maximum Mark: 7] (Do not use GDC)

. Find \(\int x \tan ^{-1} x d x \)
Answer : \( \frac{1}{2}\left(x^2 \tan ^{-1} x+\tan ^{-1} x-x\right)+c\)
. \( \) .

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. Find\( \int \frac{\ln x}{x^5} d x\)
Answer : \( -\frac{\ln x}{4 x^4}-\frac{1}{16 x^4}+C\)
. \( \) .

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Question No: 6 [Maximum Mark: 7] (Do not use GDC)

. Find \(\int x \cos 3 x d x \)
Answer : \( \frac{1}{3} x \sin 3 x+\frac{1}{9} \cos 3 x+c\)
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Question No: 7 [Maximum Mark: 7] (Do not use GDC)

. Find \(\int x \sin ^2 x d x \)
Answer : \( \frac{x^2}{4}-\frac{x}{4} \sin 2 x-\frac{\cos 2 x}{8}+c\)
. \( \) .

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Question No: 8 [Maximum Mark: 7] (Do not use GDC)

Find \( \int \sec ^3 x d x\)
Answer : \( \frac{1}{2}[\sec x \tan x+\log (\sec x+\tan x)]+c\)
. \( \) .

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Question No: 9 [Maximum Mark: 7] (Do not use GDC)

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Question No: 10 [Maximum Mark: 7] (Do not use GDC)

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Find \(\int e^{a x} \sin b x d x \)

Answer : \( \left(\frac{e^{a x}}{a^2+b^2}\right)(a \sin b x-b \cos b x)+c\)

\( \)

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Question No: 11 [Maximum Mark: 7] (Do not use GDC)

. Find \( \int e^{4 x} \cos x d x\)
Answer : \( \frac{4}{17} e^{4 x} \cos x+\frac{16}{17} e^{4 x} \sin x+c\)
. \( \) .

Question No: 1 [Maximum Mark: 7] (Do not use GDC)

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Question No: 2 [Maximum Mark: 7] (Do not use GDC)

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Question No: 4 [Maximum Mark: 7] (Do not use GDC)

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Question No: 5 [Maximum Mark: 7] (Do not use GDC)

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Question No: 6 [Maximum Mark: 7] (Do not use GDC)

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Question No: 7 [Maximum Mark: 7] (Do not use GDC)

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Question No: 8 [Maximum Mark: 7] (Do not use GDC)

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Question No: 9 [Maximum Mark: 7] (Do not use GDC)

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Question No: 10 [Maximum Mark: 7] (Do not use GDC)

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Question No: 11 [Maximum Mark: 7] (Do not use GDC)

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Question Bank : : Integration by Parts

Question No: 1 [Maximum Mark: 7] (Do not use GDC)

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Question No: 2 [Maximum Mark: 7] (Do not use GDC)

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Question No: 4 [Maximum Mark: 7] (Do not use GDC)

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Question No: 5 [Maximum Mark: 7] (Do not use GDC)

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Question No: 6 [Maximum Mark: 7] (Do not use GDC)

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Question No: 7 [Maximum Mark: 7] (Do not use GDC)

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Question No: 8 [Maximum Mark: 7] (Do not use GDC)

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Question No: 9 [Maximum Mark: 7] (Do not use GDC)

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Question No: 10 [Maximum Mark: 7] (Do not use GDC)

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Question No: 11 [Maximum Mark: 7] (Do not use GDC)

Courses

General

Contact

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