Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems ∫ e tan − 1 x ( 1 + x 2 ) [ ( sec − 1 1 + x 2 ) 2 + cos − 1 ( 1 − x 2 1 + x 2 ) ] d x \int \frac{e^{\tan^{-1} x}}{(1+x^2)} \left[ (\sec^{-1} \sqrt{1+x^2})^2 + \cos^{-1} \left( \frac{1-x^2}{1+x^2} \right) \right] dx ∫ ( 1 + x 2 ) e t a n − 1 x [ ( sec − 1 1 + x 2 ) 2 + cos − 1 ( 1 + x 2 1 − x 2 ) ] d x Mathematics
Problem ∫ e tan − 1 x ( 1 + x 2 ) [ ( sec − 1 1 + x 2 ) 2 + cos − 1 ( 1 − x 2 1 + x 2 ) ] d x \int \frac{e^{\tan^{-1} x}}{(1+x^2)} \left[ (\sec^{-1} \sqrt{1+x^2})^2 + \cos^{-1} \left( \frac{1-x^2}{1+x^2} \right) \right] dx ∫ ( 1 + x 2 ) e t a n − 1 x [ ( sec − 1 1 + x 2 ) 2 + cos − 1 ( 1 + x 2 1 − x 2 ) ] d x x > 0 x > 0 x > 0 e tan − 1 x ⋅ tan − 1 x + C e^{\tan^{-1} x} \cdot \tan^{-1} x + C e t a n − 1 x ⋅ tan − 1 x + C e tan − 1 x ⋅ ( tan − 1 x ) 2 2 + C \frac{e^{\tan^{-1} x} \cdot (\tan^{-1} x)^2}{2} + C 2 e t a n − 1 x ⋅ ( t a n − 1 x ) 2 + C e tan − 1 x ⋅ ( sec − 1 ( 1 + x 2 ) ) 2 + C e^{\tan^{-1} x} \cdot (\sec^{-1}(\sqrt{1+x^2}))^2 + C e t a n − 1 x ⋅ ( sec − 1 ( 1 + x 2 ) ) 2 + C e tan − 1 x ⋅ ( csc − 1 ( 1 + x 2 ) ) 2 + C e^{\tan^{-1} x} \cdot (\csc^{-1}(\sqrt{1+x^2}))^2 + C e t a n − 1 x ⋅ ( csc − 1 ( 1 + x 2 ) ) 2 + C Browse the problem library