Integration by substitution – Question Bank ( Qn 1 – 10)

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

Use Integration by substitution to find \( \int\left(x^2+5 x+3\right)^7(2 x+5) d x\)
Answer : \( \int\left(x^2+5 x+3\right)^7(2 x+5) d x=\frac{\left(x^2+5 x+3\right)^8}{8}+c\)
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Question No: 2 [ Maximum Mark: 7 ] (Do not use GDC)

Use integration by substitution to find \( \int 5 x^4\left(x^5+2\right)^3 d x\)
Answer : \( \int 5 x^4\left(x^5+2\right)^3 d x=\frac{\left(x^5+2\right)^4}{4}+c\)
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Question No: 3 [ Maximum Mark: 7 ] (Do not use GDC)

Use integration by substitution to find \( \int\left(x^2-2\right)\left(x^3-6 x+5\right)^{10} d x\)
Answer : \(\int\left(x^2-2\right)\left(x^3-6 x+5\right)^{10} d x=\frac{1}{33}\left(x^3-6 x+5\right)^{11}+c \)
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Question No: 4 [ Maximum Mark: 7 ] (Do not use GDC)

Use integration by substitution to find \(\int\left(x^3-5\right) \sqrt{\left(x^4-20 x+6\right)} d x \)
Answer : \( \int \sqrt{x^4-20 x+6}\left(x^3-5\right) d x=\frac{1}{6}\left(x^4-20 x+6\right)^{3 / 2}+c\)
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.Question No: 5 [ Maximum Mark: 7 ] (Do not use GDC)

Use integration by substitution to find \( \int 2 x e^{x^2+1} d x\)
Answer : \( \int 2 x e^{x^2+1} d x=e^{x^2+1}+c\)
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