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∫−π2π2[esin(x)cos(x)] dx=a−1a, a>0, a= ?\large \int_{-\frac \pi 2 }^{\frac \pi 2 } \bigg [ e^{ \sin(x)} \cos (x )\bigg ] \ dx = a - \frac 1 a, \ \ \ a > 0, \ \ \ \ \ a = \ ? ∫−2π2π[esin(x)cos(x)] dx=a−a1, a>0, a= ?
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∫1ax−1x+xdx=4\large\int_{1}^{a}\dfrac{x-1}{x+\sqrt{x}}dx=4∫1ax+xx−1dx=4
Let a>1a>1a>1 be a constant satisfying the equation above. What is the value of a2+a+1\large a^2+a+1a2+a+1?
Evaluate the following integral
∫sin(x)cos3(x) dx\large\displaystyle \int \dfrac{\sin(x)}{\cos^3(x)} \, \Bbb{d}x ∫cos3(x)sin(x)dx
∫02x1−(x−1)2 dx= ? \int_0^2 x \sqrt{1-(x-1)^2} \, dx = \, ? ∫02x1−(x−1)2dx=?
Give your answer to 2 decimal places.
Evaluate the indefinite integral below.
∫dx1+e−x\large \int \frac{dx}{1 + e^{-x}}∫1+e−xdx
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