3
∫ f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)
∫ f'(x)/( q2f(x)2 - p2) dx = [1/(2pq)ln[(qf(x) - p)/(qf(x) + p)]
0.5
∫ f'(x)/√[f(x)2 + a] dx = ln[f(x) + √(f(x)2 + a)] + C C is the constant of integration.
The indefinite integral of (1/x^2)*dx is -1/x+C.
3
For it to be a definite integral, you would need to specify a range. We can however give you the indefinite integral. The easiest way to do this is to think of it not as a fraction, but as a negative exponent: 1/x2 = x-2 It then becomes quite easy to integrate, as we can say in general: ∫(axn) dx = ax(n + 1) / (n + 1) + C In this case then, we have: ∫(x-2) dx = -x-1 + C, or -1/x + C
∫ f'(x)/[f(x)√(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C C is the constant of integration.
∫ f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)
∫ f'(x)/√(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.
- ln ((x^2)-4)
∫ f'(x)/( q2f(x)2 - p2) dx = [1/(2pq)ln[(qf(x) - p)/(qf(x) + p)]
The square root of ( a squared plus b squared ), quantity divided by a, where a is the length of the semi-major axis and b is the length of the semi-minor axis.
The square root of ( a squared plus b squared ), quantity divided by a, where a is the length of the semi-major axis and b is the length of the semi-minor axis.
integral of radical sinx
The square root of ( a squared plus b squared ), quantity divided by a, where a is the length of the semi-major axis and b is the length of the semi-minor axis.