Question

Integrate 2x cos (x2 – 5) with respect to x .

Answer 1

Step-by-step explanation:

Given:$\int 2x\:cos(x^2-5)\:dx$

To find: Evaluate the integral.

Solution:

Step 1: Prepare given expression for integration.

Let (x²-5)=t

So,

2x dx=dt

Substitute the values

$\int cos\:t\:dt$

Step 2: Evaluate the integral with respect to t.

$\int\:cos\:t \:dt=sin \:t +C$

Step 3: Undo substitution

put t=x²-5

$\int 2x cos(x^2-5) dx= sin(x^2-5)+C$

Final answer:

$\bold{\red{\int 2x\:cos(x^2-5)\:dx= sin(x^2-5)+C}}$

Hope it helps you.

To learn more:

$\displaystyle \int_0^{ \frac{\pi}{2} } cos^5 x\ dx = \:?\:$

Solve the math by " Wallie's theorem " with expl...

https://brainly.in/question/40749419

Answer 2

Given :  2x cos (x² – 5)

To Find : Integrate with respect to x .

Solution:

∫2x cos (x² – 5)  dx

substitute x² – 5 = y

=> 2xdx = dy

= ∫  cosy dy

= siny  +  C

= sin(x² – 5)  + C

∫2x cos (x² – 5)  dx = sin(x² – 5)  + C

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