Solve this: Q ∫dx4+sin 2x2 = - Maths - Integrals

Question

Solve this:
Q ∫ d x 4 + sin   2 x 2 =

Neha Sethi · Accepted Answer

Dear student
∫dx4+sin2x2=∫dx4+sin22xPut u=2x⇒dx=du2=12∫14+sin2uduConsider,∫14+sin2uduUse sinu=tanusecuAlso, sec2u=1+tan2u=∫sec2u×15tan2u+4duPut v=tanu⇒du=1sec2udv=∫15v2+4dvPut w=5v2⇒dv=25dw=∫254w2+4dw=125∫11+w2dw=tan-1w25=tan-15v225=tan-15tanu 225Putting in solved integrals,12∫14+sin2udu=tan-15tanu 245=tan-15tan2x 245+C
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Solve this: Q. ∫ d x 4 + sin 2 x 2 =

Solve this:
Q. $\int \frac{d x}{4 + {(\sin 2 x)}^{2}}$ =