Okh to solve your question I will use

i for integration and d for diffrentiation w.r.t. x okh

Apply ILATE rule

which says i= log(e^x+1) i e^xdx- i { d (log(e^x+1)) i e^xdx}dx

log(e^x+1)e^x- i {e^x/(e^x+1)*e^x}dx ( i e^x=e^x && d logx=1/x)

Now use substitution

[Let u=e^x then du=e^xdx]

The

Hello aspirant,

√(tan x) dx

Let tan x = t 2

⇒ sec 2 x dx = 2t dt

⇒ dx = [2t / (1 + t 4 )]dt

⇒ Integral  ∫ 2t 2 / (1 + t 4 ) dt

⇒ ∫[(t 2 + 1) + (t 2 -

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Government

Indian Institute of Technology Gandhinagar

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LD College of Engineering, Ahmedabad

Private

Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar

Nirma University, Ahmedabad

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