Evaluate -3 x-4x2-8 x-15 d xwhere C is constant of integration

Let I=∫3 x+4x^2 8 x+15 d x ⇒ I=∫3 x+4(x 3)(x 5) d x Using partial fraction 3 x+4(x 3)(x 5)=Ax 3+Bx 5 ⇒ A= 132 , B=192 ∴ I= 132∫dxx 3+192 nbsp;∫d xx 5 ⇒ I= ...

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Byju's Answer

Standard XII

Mathematics

Solving Linear Differential Equations of First Order

Evaluate ∫3 x...

Question

Evaluate $\int \frac{3 x + 4}{x^{2} - 8 x + 15} d x$
(where $C$ is constant of integration)

- \frac{19}{2} ln | x - 3 | + \frac{13}{2} ln | x - 5 | + C

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\frac{13}{2} ln | x - 3 | - \frac{19}{2} ln | x - 5 | + C

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- \frac{13}{2} ln | x - 3 | + \frac{19}{2} ln | x - 5 | + C

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\frac{19}{2} ln | x - 3 | - \frac{13}{2} ln | x - 5 | + C

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Solution

The correct option is C $- \frac{13}{2} ln | x - 3 | + \frac{19}{2} ln | x - 5 | + C$
Let $I = \int \frac{3 x + 4}{x^{2} - 8 x + 15} d x$
$\Rightarrow I = \int \frac{3 x + 4}{(x - 3) (x - 5)} d x$
Using partial fraction
$\frac{3 x + 4}{(x - 3) (x - 5)} = \frac{A}{x - 3} + \frac{B}{x - 5}$

$\Rightarrow A = - \frac{13}{2}, B = \frac{19}{2}$

$∴ I = - \frac{13}{2} \int \frac{d x}{x - 3} + \frac{19}{2} \int \frac{d x}{x - 5}$

$\Rightarrow I = - \frac{13}{2} ln | x - 3 | + \frac{19}{2} ln | x - 5 | + C$

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Evaluate ∫3x+4x2−8x+15dx (where C is constant of integration)

The correct option is C −132ln|x−3|+192ln|x−5|+CLet I=∫3x+4x2−8x+15dx ⇒I=∫3x+4(x−3)(x−5)dx Using partial fraction 3x+4(x−3)(x−5)=Ax−3+Bx−5 ⇒A=−132,B=192 ∴I=−132∫dxx−3+192∫dxx−5 ⇒I=−132ln|x−3|+192ln|x−5|+C

Evaluate $\int \frac{3 x + 4}{x^{2} - 8 x + 15} d x$
(where $C$ is constant of integration)