Mathematics

Solve:
$$\int {\sin x\left( {2 + 5x} \right)} dx$$


SOLUTION
$$\displaystyle\int \sin x(2+5x)dx=\displaystyle\int (2\sin x+5x\sin x)dx$$

$$=\displaystyle\int 2\sin xdx+\displaystyle\int 5x\sin xdx$$

$$=-2\cos x+5\left[x\displaystyle\int \sin x dx-\displaystyle\int\left\{\dfrac{d}{dx}(x)\displaystyle\int \sin x dx\right\}dx\right]$$

$$=-2\cos x+5\left[x(-\cos x)-\displaystyle\int (-\cos x)dx\right]$$
$$=-2\cos x+5\left[-x\cos x+\displaystyle\int\cos xdx\right]$$

$$=-2\cos x-5x\cos x+5\sin x+c$$

$$\displaystyle\int \sin x(2+5x)dx=5\sin x-2\cos x-5x\cos x+c$$.
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Solve
$$\int \dfrac{\cos (x+a)}{\cos (x-a)} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate: $$\int \dfrac {e^{\log \sqrt {x}}}{x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
The value of $$\displaystyle\int _{ 0 }^{ \tfrac { \pi  }{ 2 }  }{ \frac { \cos ^{ \frac { 5 }{ 3 }  }{ x }  }{ \cos ^{ \frac { 5 }{ 3 }  }{ x } +\sin ^{ \frac { 5 }{ 3 }  }{ x }  } dx } $$ is
  • A. $$\dfrac { \pi }{ 2 } $$
  • B. $$0$$
  • C. $$\pi$$
  • D. $$\dfrac { \pi }{ 4 } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
$$\displaystyle \int \dfrac {x-\sin x}{1-\cos x}dx=$$
  • A. $$x \cot \dfrac {x}{2}+C$$
  • B. $$\cot \dfrac {x}{2}+C$$
  • C. $$None\ of\ these$$
  • D. $$-x \cot \dfrac {x}{2}+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 TRUE/FALSE Medium
If $$f,g,h$$ be continuous functions on $$[0,a]$$ such that $$f(a-x)=-f(x),g(a-x)=g(x)$$ and $$3h(x)-4h(a-x)=5$$ then  $$\displaystyle \int_0^a f(x)g(x)h(x)dx=0$$
  • A. False
  • B. True

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer