C

1003107913

Level: 
C
Which method is the most effective to solve the indefinite integral ∫sin⁡(ln⁡x)dx in the range (0;∞)?
By parts integration, when we let u(x)=sin⁡⁡(ln⁡⁡x), where u(x) is the integrated function, and we let v′(x)=1, where v′(x) is the differentiated function.
By substitution, a=sin⁡⁡x.
By parts integration, when we let u(x)=ln⁡x, where u(x) is the integrated function, and we let v′(x)=sin⁡x, where v′(x) is the differentiated function.
By substitution, t=sin⁡⁡(ln⁡⁡x).

1003107912

Level: 
C
Which method is the most effective to solve the indefinite integral ∫dxxln⁡⁡x in the range (1;∞)?
By substitution, a=ln⁡⁡x.
By parts integration, when we let u(x)=1x, where u(x) is the integrated function, and we let v′(x)=ln⁡⁡x, where v′(x) is the differentiated function.
By substitution, a=1x.
By factorization into ∫1xdx⋅∫1ln⁡⁡xdx.

1003107905

Level: 
C
Solve the indefinite integral ∫(abec−bx2+5b−sin⁡⁡c)dc of a real-valued function, where a, b, x are real numbers.
abec−bcx2+c⋅5b+cos⁡⁡c+k, k∈R
ec−cos⁡⁡c+k, k∈R
abec−bcx2+c⋅5b−cos⁡⁡c+k, k∈R
abec−bcx2+5b⋅c−sin⁡⁡c+k, k∈R