∫(1 + 3√x + 5x)dx

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / ∫(1 + 3√x + 5x)dx

926 views

∫(1 + 3√x + 5x)dx

For each term the aim is to raise the power of x by 1 and divide by the new power.

For this question, each part of the expression can be looked at seperately to make things a bit easier:

∫(1 + 3√x + 5x)dx = ∫1dx + ∫3√xdx + ∫5xdx

The first part of the expression can be looked at as 1*x⁰, so the integral of this is 1*x = x

The second part is a bit more difficult as the power of x isnt a whole number so it can be written as 3*x^1/2, the integral of this being 3*x^3/2*(2/3) = 2x^3/2, (the 2/3 comes from dividing by the new power).

Finally the integral of 5x is easier as the power of x is a whole number and so is easily calculated as 5/2*x².

Then finally recombining the three part the final answer is:

∫(1 + 3√x + 5x)dx = x + 2x^3/2 + (5/2)x²+ c

(c is constant and can take any value, this isnt a majorly important part of the question)

Mary T. A Level Maths tutor, GCSE Maths tutor

2 years ago

Answered by Mary, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

350 SUBJECT SPECIALISTS

Scott R. GCSE Maths tutor, 13 Plus Maths tutor, A Level Maths tutor,...

View profile

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

5.0

36 reviews | 96 completed tutorials

Save profile

Samuel C. A Level Physics tutor, A Level Maths tutor, A Level Further...

View profile

£26 /hr

Samuel C.

Degree: Physics (Bachelors) - Durham University

Subjects offered:Maths, Physics+ 2 more

“Hi, I'm Sam Crawford. I'm studying Maths and Physics at Durham University, with an offer from Cambridge for next year, and I absolutely love both subjects.”

5.0

85 reviews | 165 completed tutorials

Save profile

Edoardo M. A Level Maths tutor, IB Maths tutor, GCSE Maths tutor

View profile

£26 /hr

Edoardo M.

Degree: Mathematics (Bachelors) - Bath University

Subjects offered:Maths, .STEP.

“Hi! My name is Edoardo, and I'm a Maths student at the University of Bath. I would be really excited to start working with you. ”

4.9

50 reviews | 55 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

Mary T.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths

“About me: I am currently studying maths in my first year at Durham University. Not only do I have a love for my subject but also for teaching it. In my last year of sixth form I set up a school wide tutoring system which helped many ...”

5.0

3 reviews | 13 completed tutorials

Save profile

Version:	3.49.4
Build:	b2e05e7dfef3
Time:	2017-08-18T11:35:22Z

MYTUTOR SUBJECT ANSWERS

∫(1 + 3√x + 5x)dx

Still stuck? Get one-to-one help from a personally interviewed subject specialist

350 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips