Evaluate: $\int e^{\sin^{-1}x}\cdot\frac{x+\sqrt{1-x^2}}{\sqrt{1-x^2}}\,dx$

Evaluate: ∫ e^sin⁻¹x·fracx+√(1-x²)√(1-x²)dx

3.3 · Q146

\int e^{\sin^{-1}x}\cdot\frac{x+\sqrt{1-x^2}}{\sqrt{1-x^2}}\,dx

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

76% · 195/255 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Let $t=\sin^{-1}x$ , so $x=\sin t$ , $\sqrt{1-x^2}=\cos t$ , $dx=\cos t\,dt$ :

$\int e^{\sin^{-1}x}\cdot\dfrac{x+\sqrt{1-x^2}}{\sqrt{1-x^2}}\,dx=\int e^t\cdot\dfrac{\sin t+\cos t}{\cos t}\cdot\cos t\,dt=\int e^t(\sin t+\cos t)\,dt$ …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ145 — Evaluate: ∫ e5x·(5xlog x+1)/(x)dx →Next questionQ147 — Evaluate: ∫ (log(1+x))/(1+x)dx

Q.Evaluate: $\int e^{\sin^{-1}x}\cdot\frac{x+\sqrt{1-x^2}}{\sqrt{1-x^2}}\,dx$

Concept understanding — Integral of the Form ∫ eˣ[f(x) + f'(x)] dx

Q.Evaluate: ∫esin⁡−1x⋅x+1−x21−x2 dx\int e^{\sin^{-1}x}\cdot\frac{x+\sqrt{1-x^2}}{\sqrt{1-x^2}}\,dx∫esin−1x⋅1−x2​x+1−x2​​dx

🎓Unlock everything free for 14 days

Q.Evaluate: $\int e^{\sin^{-1}x}\cdot\frac{x+\sqrt{1-x^2}}{\sqrt{1-x^2}}\,dx$

Unlock everything free for 14 days