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Evaluate: (i) int((1+x)^3)/(sqrt(x))\ ...

Evaluate:
(i) `int((1+x)^3)/(sqrt(x))\ dx`
(ii) `int{x^2+e^(logx)+(e/2)^x}\ dx`

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Let's solve the given integrals step by step. ### (i) Evaluate \( \int \frac{(1+x)^3}{\sqrt{x}} \, dx \) **Step 1: Expand the integrand** First, we expand \( (1+x)^3 \): \[ ...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
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  2. Evaluate: int(m/x+x/m+m^x+x^m+m x)\ dx (ii) int(sqrt(x)-1/(sqrt(x)))^2...

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  5. Evaluate: (i) int1/(sqrt(x))(1+1/x)\ dx (ii) int(x^6+1)/(x^2+1)\ dx

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  7. Evaluate: (i) intsqrt(x)(3-5x)\ dx (ii) int((x+1)(x-2))/(sqrt(x))\ d...

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  8. Evaluate: (i) int(x^5+x^(-2)+2)/(x^2)\ dx (ii) int(5\ x^4+12\ x^3+7...

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  9. Evaluate: (i) int(sin^2x)/(1+cosx)\ dx (ii) int(sec^2x+cos e c^2x)\...

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  12. Evaluate: (i) int(cosx)/(1-cosx)\ dx (ii) int(cos^2x-sin^2x)/(sqrt...

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  13. Evaluate: (i) int1/(1-cosx)\ dx (ii) int1/(1-sinx)\ dx

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  17. Evaluate: (i) intcot^(-1)((sin2x)/(1-cos2x))\ dx (ii) intsin^(-1)((2...

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