integral of 1/(nsqrt(n^2-1))

解答

\int \frac{1}{n n ^{2} - 1} d n

arctan (n^{2} - 1) + C

求解步骤

\int \frac{1}{n n ^{2} - 1} d n

使用换元积分法

= \int \frac{1}{u ^{2} + 1} d u

使用积分常见定则:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= arctan (u)

u = n^{2} - 1

代回

= arctan (n^{2} - 1)

解答补常数

= arctan (n^{2} - 1) + C

d er i v a t i v e cos (e^{x^{5} c o s (x)})

\int_{6}^{8} \frac{96}{( x - 6 ) ^{3}} d x

\int e^{3 x} \cdot x d x

a re a y = sin^{2} (x), y = sin^{3} (x), 0 \leq x \leq π

[x^{2} + y^{2}] d x = x y d y