MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration by Substitution

Solve: ∫5x-...

Question

Solve: $\int \frac{5 x - 2}{1 + 2 x + 3 x^{2}} . d x$

Open in App

Solution

$\int \frac{5 x - 2}{1 + 2 x + 3 x^{2}} d x l e t, u = 5 x - 2 ∴ \int \frac{5 x - 2}{1 + 2 x + 3 x^{2}} d x = \int \frac{5 u}{3 u^{2} + 22 u + 57} d u = 5 \int \frac{u}{3 {(u + \frac{11}{3})}^{2} + \frac{50}{3}} d u a g a i n, l e t v = u + \frac{11}{3} ∴ 5 \int \frac{u}{3 {(u + \frac{11}{3})}^{2} + \frac{50}{3}} d u = 5 \int \frac{3 v - 11}{9 v^{2} + 50} d v s u b s t i t u t i n g, v = \frac{5 \sqrt{2}}{3} w ∴ \int \frac{3 v - 11}{9 v^{2} + 50} d v = 5. \int \frac{5. \sqrt{2} w - 11}{15 \sqrt{2} (w^{2} + 1)} d w = \frac{5}{15 \sqrt{2}} (\int \frac{5 \sqrt{2}}{w^{2} + 1} d w - \int \frac{11}{w^{2} + 1} d w) = \frac{5}{15 \sqrt{2}} [\frac{5}{\sqrt{2}} l o g (\frac{3}{5 \sqrt{2}} {((5 x - 2 + \frac{11}{3}))}^{2}) - 11 arctan \frac{3}{5 \sqrt{2}} ((5 x - 2 + \frac{11}{3}))] + C = \frac{1}{6} [5 l o g (\frac{{(3 x + 1)}^{2}}{2} + 1) - 11 \sqrt{2} arctan (\frac{3 x + 1}{\sqrt{2}})] + C$

Suggest Corrections

thumbs-up

0

Similar questions

\int \frac{2 x^{3} - 3 x^{2} - 8 x - 26}{2 x^{2} - 5 x + 2} . d x

Solve :- $(3 x^{2} + 5 x - 7) (x - 1) - (x^{2} - 2 x + 3) (x + 4)$

\int (1 + 2 x + 3 x^{2} + 4 x^{3} + . . . . . .) d x

(| x | < 1)

.

Q. Solve the following inequality:

\sqrt{3 x^{2} + 5 x + 7} - \sqrt{3 x^{2} + 5 x + 2} > 1.

\int_{0}^{1} \frac{2 x + 3}{5 x^{2} + 1} d x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Integration by Substitution

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Integration by Substitution

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon