Question Type 2: Integrals of derivatives of reciprocal trigonometric functions in composite forms Exercises

Evaluate $\displaystyle \int -\csc(\sin x)\cot(\sin x)\cos x\,dx$.

Find $\displaystyle \int 5\sec(4x)\tan(4x)\,dx$.

Find $\displaystyle \int -6\csc(3x)\cot(3x)\,dx$.

Calculate $\displaystyle \int\bigl[\sec(5x)\tan(5x)-\csc(5x)\cot(5x)\bigr]\,dx$.

Find $\displaystyle \int \sec(7x)\tan(7x)\,dx$.

Find $\displaystyle \int \sec(\sin x)\tan(\sin x)\cos x\,dx$.

Find $\displaystyle \int \sec(\ln x)\tan(\ln x)\frac{1}{x}\,dx$.

Find $\displaystyle \int e^{x}\sec(e^{x})\tan(e^{x})\,dx$.

Evaluate $\displaystyle \int \csc(5x)\cot(5x)\,dx$.

Evaluate $\displaystyle \int -\csc(3x^{2})\cot(3x^{2})\,6x\,dx$.

Compute $\displaystyle \int\sec(5x^{3})\tan(5x^{3})\,15x^{2}\,dx$.

Evaluate $\displaystyle \int -3\csc(6x)\cot(6x)\,dx$.

Find $\displaystyle \int 4\sec(2x)\tan(2x)\,dx$.

Evaluate $\displaystyle \int\bigl[\sec(2x)\tan(2x)+\csc(2x)\cot(2x)\bigr]\,dx$.

Find the indefinite integral: $\displaystyle \int \sec(3x)\tan(3x)\,dx$

Evaluate $\displaystyle \int\bigl[6\sec(2x)\tan(2x)-3\csc(2x)\cot(2x)\bigr]\,dx$.