MYTUTOR SUBJECT ANSWERS

822 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*x1/2, the integral of this being     3*x3/2*(2/3) = 2x3/2, (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 + 2x3/2 + (5/2)x+ 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

1 year ago

Answered by Mary, an A Level Maths tutor with MyTutor


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

302 SUBJECT SPECIALISTS

£20 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
.STEP.
.MAT.
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

£20 /hr

Mustafa A.

Degree: Economics (Bachelors) - Birmingham University

Subjects offered:Maths, Economics

Maths
Economics

“Highly proficient Maths and Economics tutor who's goal is to ensure that the student comes from a session with the ability to tackle the problem with ease.”

MyTutor guarantee

£22 /hr

Ben T.

Degree: Engineering (Bachelors) - Cambridge University

Subjects offered:Maths, Physics+ 4 more

Maths
Physics
French
Chemistry
-Personal Statements-
-Oxbridge Preparation-

“Hi there! I’m your friendly neighbourhood Cambridge grad, brimming with tricks and enthusiasm for Maths, Sciences and French. To learn more, view my profile...”

About the author

Mary T.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths

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 ...”

You may also like...

Other A Level Maths questions

What values of θ between 0 and 2π satisfy the equation cosec(θ) + 5cot(θ) = 3sin(θ)?

Use the substitution u = 6 - x^2 to find the value of the integral of (x^3)/(sqrt(6-x^2)) between the limits of x = 1 and x = 2 (AQA core 3 maths

y=e^(2x) - x^3. Find dy/dx. (please note this is "e to the power of 2x, minus x cubed")

Is a line ax+by+c=0 tangent to a circle?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok