Let -dx-x2008 - x - 1-p ln-xq-1 - xr- - C where p- q- r - N and need not be distinct- then the sum of the digit in value of p - q - r equals

I = #160; ∫dx/x(x^2007 + 1) = #160;∫x^2007 + 1 #160;x^2007/x(x^2007 + 1) #160;dx = ∫ [1/x x^2006/1 + x^2007] dx = ln x 1/2007 ln(1 + ...

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Byju's Answer

Standard XII

Mathematics

Functions

Let ∫dx/x20...

Question

Let $\int \frac{d x}{x^{2008} + x} = \frac{1}{p} l n [\frac{x^{q}}{1 + x^{r}}] + C$ where p, q, r $\in$ N and need not be distinct, then the sum of the digit in value of (p + q + r) equals

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Solution

I = $\int \frac{d x}{x (x^{2007} + 1)} = \int \frac{x^{2007} + 1 - x^{2007}}{x (x^{2007} + 1)} d x$
= $\int [\frac{1}{x} - \frac{x^{2006}}{1 + x^{2007}}] d x$
= ln x - $\frac{1}{2007} l n (1 + x^{2007}) d x$
= $\frac{l n x^{2007} - l n (1 + x^{2007})}{2007} = \frac{1}{2007} l n [\frac{x^{2007}}{1 + x^{2007}}] + C$
p + q + r = 6021 = 9

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Let $\int \frac{d x}{x^{2008} + x} = \frac{1}{p} l n (\frac{x^{q}}{1 + x^{r}}) + C$ where $p, q, r ϵ N$ and need not be distinct, then the value of (p+q+r) equals

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Let ∫dxx2008+x=1pln[xq1+xr]+C where p, q, r ∈ N and need not be distinct, then the sum of the digit in value of (p + q + r) equals

I = ∫dxx(x2007+1)=∫x2007+1−x2007x(x2007+1)dx= ∫[1x−x20061+x2007]dx= ln x - 12007ln(1+x2007)dx= lnx2007−ln(1+x2007)2007=12007ln[x20071+x2007]+Cp + q + r = 6021 = 9

Let $\int \frac{d x}{x^{2008} + x} = \frac{1}{p} l n [\frac{x^{q}}{1 + x^{r}}] + C$ where p, q, r $\in$ N and need not be distinct, then the sum of the digit in value of (p + q + r) equals