Learn Exercise 7.4 with Free Lessons & Tips

Question 1:

Integrate the following

Solution 1:

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Anubhav Singh

Question 2:

Integrate the function

$\frac{1}{9x^{2}+6x+5}$

Solution 2:

$\frac{1}{9x^{2}+6x+5}$ = $\int \frac{1}{(3x+1)^{2}+2^{2}}dx$

Let (3x+1) =t

$\therefore 3dx=dt$

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Tasneem

Question 3:

Integrate the function

Solution 3:

Let x³ = t

∴ 3x²dx = dt

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Shivam Sharma

Question 4:

Integrate the function

Solution 4:

Let 2x = t

∴ 2dx = dt

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Shivam Sharma

Question 5:

Integrate the function

Solution 5:

Let 2 − x = t

⇒ −dx = dt

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Shivam Sharma

Question 6:

Integrate the function

Solution 6:

Let 5x = t

∴ 5dx = dt

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Tasneem

Question 7:

Integrate the function

Solution 7:

Let $x^{2}=t$

So $2xdx=dt$

$\int \frac{3x}{1+2x^{4}} dx=\int \frac{1.5dt}{1+2t^{2}}$

$= 0.75\int \frac{dt}{t^{2}+0.5}$

$\frac{0.75}{0.5^{0.5}}tan^{-1}(\frac{t}{0.5^{0.5}})$

$1.06tan^{-1}(1.414x^{2})$ + c

where c is used for integration constant

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Soumyajit Gangopadhyay

Question 8:

Integrate the function

Solution 8:

Let x³ = t

∴ 3x²dx = dt

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Shivam Sharma

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Learn Exercise 7.4 with Free Lessons & Tips

All Exercises - Chapter 7 - Integrals

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