Evaluate the integration of : (co3x-x^2)(sin3x-x^3)dx?

Question

Evaluate the integration of : (co3x-x^2)(sin3x-x^3)dx?

1 Answer

Impact of this question

1232 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-01T13:51:55

$I = \frac{1}{3} ln (∣ ∣ sin (3 x) - x^{3} ∣ ∣) + C$ $I=1/3ln(abs(sin(3x)-x^3))+C$

Explanation:

We want to solve

$I = \int \frac{cos (3 x) - x^{2}}{sin (3 x) - x^{3}} d x$ $I=int(cos(3x)-x^2)/(sin(3x)-x^3)dx$

Make a substitution

$u = sin (3 x) - x^{3} \Rightarrow d u = 3 (cos (3 x) - x^{2}) d x$ $color(blue)(u=sin(3x)-x^3=>du=3(cos(3x)-x^2)dx$

$I = \int \frac{cos (3 x) - x^{2}}{u \cdot 3 (cos (3 x) - x^{2})} d u$ $I=int(cos(3x)-x^2)/(u*3(cos(3x)-x^2))du$

$I = \frac{1}{3} \int \frac{1}{u} d u$ $color(white)(I)=1/3int1/udu$

$I = \frac{1}{3} ln (| u |) + C$ $color(white)(I)=1/3ln(abs(u))+C$

Substitute back $u = sin (3 x) - x^{3}$ $color(blue)(u=sin(3x)-x^3)$

$I = \frac{1}{3} ln (∣ ∣ sin (3 x) - x^{3} ∣ ∣) + C$ $I=1/3ln(abs(sin(3x)-x^3))+C$

Science

Math

Humanities

... and beyond

Evaluate the integration of : (co3x-x^2)(sin3x-x^3)dx?

1 Answer

Explanation:

Related questions

Impact of this question